Notes on the Vaiṣṇava

Source: here.

Notes on the Vaiṣṇava retinue deities-1

Nature of viṣvaksena

The śaiva pattern of worship,
which is especially emphasized in the Iśāna-srotas (siddhānta),
features the Nirmālya-devatā, Caṇḍeśvara
with roots in the older Pāśupata atimārga.
This deity receives offerings, such as leaves and flowers, that have been initially offered to Rudra-sadāśiva.
In the śaiva-saura system,
he appears as Tejaścaṇḍa,
the Nirmālya-devatā of Sūrya.

The Vaikhānasa and Pāñcarātrika systems of the Vaiṣṇava tradition also have an equivalent deity in the form of Viṣvaksena.
However, we posit in this note that he also encompasses to a degree features of the ape-faced śaiva deity Nandin (sometimes bull-faced, especially in the later reflexes of the tradition),
who is one of the great gaṇeśvara-s of Rudra’s hordes,
and the sons of Rudra, the gods Skanda and Vināyaka.+++(5)+++

Sources

His worship is laid out in multiple Pāñcarātrika tantra-s. Below we shall primarily consider aspects of his worship taught in one of the older Pāñcarātrika texts, the Pauṣkara-saṃhitā, and the Śakti (Śrī)-oriented Pāñcarātrika text, the Lakṣṃī-tantra, along with parallels drawn from the Jayākhya-samhitā, another old tantra of the Pañcarātra-s.

The Pauṣkara is presented as the teaching of the Bhagavant (Viṣṇu) to Pauṣkara (the lotus-born one, i.e., Brahman).
Its colophon calls it the Pauṣakara-saṃhitā from the Mahopaniṣat of the Pāñcarātra.
Despite this appellation,
it resembles a rather standard tāntrika text in its structure and style of presentation.
The two versions of the Pauṣkara that we used for this note have corruptions and lacunae,
some of which might have crept into the transliterations presented below
despite our attempts at restoration.

Ectype of Vāsudeva

The name Viṣvaksena appears for the first time in the Mahābhārata
and is associated with the Sāttvata strand of the proto-Pāñcarātrika tradition.
There, it is used primarily as a name or an ectype of the Vāsudeva.
Examples of this include the Viṣṇu-sahasra-nāma and the Viṣvaksena-stuti found in the Anuśāsana-parvan (“Critical” 13.143).
In the latter, it is made clear that the Vāsudeva, equated with the Sāttvata hero,
is the source and resort of everything (Vedic rituals etc.) in his Viṣvaksena manifestation:

वेदांश् च यो वेदयते ऽधिदेवो
विधींश् च यश् चाश्रयते पुराणान् ॥
कामे वेदे लौकिके यत् फलं च
विष्वक्सेने सर्वम् एतत् प्रतीहि ॥
ज्योतींषि शुक्लानि च सर्वलोके ।
त्रयो लोका लोकपालास् त्रयश् च ॥
त्रयो ऽग्नयो व्याहृतयश् च तिस्रः ।
सर्वे देवा देवकीपुत्र एव ॥
संवत्सरः स ऋतुः सो ऽर्धमासः ।
सो ऽहोरात्रः स कला वै स काष्ठाः ॥
मात्रा मुहूर्ताश् च लवाः क्षणाश् च ।
विष्वक्सेने सर्वम् एतत् प्रतीहि ॥
चन्द्रादित्यौ ग्रह-नक्षत्र-ताराः ।
सर्वाणि दर्शान्य् अथ पौर्णमास्यः ॥
नक्षत्र-योगा ऋतवश् च पार्थ ।
विष्वक्सेनात् सर्वम् एतत् प्रसूतम् ॥

Again, in the Harivaṃśa we encounter Viṣvaksena used in the same sense in the early Pāñcarātrika mantra of 101 words and 367 syllables (symbolizing Viṣnu as the year) taught by Kaśyapa found in its Appendix.+++(5 ??)+++

The same sense is seen in the Viṣṇu-gāyatrī that was used by the Kaṭha-s of the Panjab and Kashmir in their daily worship following the manual of Laugākṣī (in place of the Nārāyaṇa-gāyatrī of the Taittirīyaka-s):

viśvarūpāya vidmahe viṣvaksenāya dhīmahi । tanno viṣṇuḥ pracodayāt ॥

Transition

This continues into the purāṇa-s such as the Padmapurāṇa,
where the name is used in the above sense in several stuti-s dedicated to Viṣṇu. Thus, the transformation of Viṣvaksena
from a name or an ectype of the Vāsudeva in proto-Pāñcarātra
to the Nirmālya-devatā of tāntrika Pāñcarātra happened well after the Mahābhārata, Harivaṃśa and certain Paurāṇika sections.

Nevertheless, interestingly, in the Pauṣkara-samḥitā
we have Vāsudeva expound a theology of Viṣvaksena
that hearkens back to the above stuti from the Anuśāsana-parvan.
Thus, it appears that Viṣvaksena as the nirmālya-devatā
still bears a connection to this older usage of the name (Pauṣkara-samḥitā, chapter 20):

Pauṣkara asks Viṣṇu about Viṣvaksena thusly:

ka eṣo .atulavīryo hi
yasya dūrād dravanti ca ।
vighnā nimeṣa-mātreṇa
trailokyonmūlana-kṣamāḥ ॥

Who is this, indeed of unequaled heroism, by whose mere wink obstacles capable of uprooting the triple-word melt away in the distance?

Viṣṇu answered:

klavaiśvānarākhyā yā mūrtis turyātmano vibhoḥ ।
sa eṣa dvija devaḥ syād viṣvaksenaḥ prakīrtitaḥ ॥
sthita āhavanīyādi-bhedena makha-yājinām ।
ṛk-pūtam hutam ādāya tarpayaty akhilaṃ jagat ॥
evaṃ mantra-mayād yāgāt sāttvikāt brahmabhāvitāt ।
saṃprāpya gurumūrter vai prāpaṇaṃ mantra-sat-kṛtam ॥
anāhūtāṃ surāṇāṃ ca sarva-loka-nivāsinām ।
svayaṃ saṃvibhajaty āśu tad anugraha-kāmyayā ॥

He is known as Kālavaiśvānara (the fire of the end of time), who is an emanation of the four-fold lord (i.e., the Vāsudeva with the 3 other vyūha-s). O twice-born one, he is that god who is known as Viṣvaksena. He is situated in the types of fire altars viz. Āhavanīya and the like of the Vedic ritualists. Having taken the oblations sanctified by ṛk-s, he satisfies the entire universe. Thus, obtaining [the essence] from the rituals filled with incantations, from purity, proper ritual intention and the form of the teacher, he verily gains the good deeds of the mantra [deployment]. And he himself quickly apportions these to the uninvoked gods dwelling in all the worlds with the intention of gaining their favor.

Representation

In terms of the temple ritual, in addition to the contruction of a Viṣvaksena shrine within the third circuit of the Viṣṇu complex, he may be housed in a separate temple to the south of a village (Sanatkumāra-saṃhitā).
His worship in these shrines is accompanied by a special dance and music.+++(5)+++
The emergence of Viṣvaksena as the Nirmālya-devatā seems to have led to a special group of priestly assistants, the kārin-s, who partake of the final offerings handed over to Viṣvaksena.+++(5)+++

yantra and position

The yantra of Viṣvaksena (Pauṣkara, chapter 20):

dharmādy ananta-paryantaṃ pañcakaṃ navakaṃ tu vā ।
sattvenācchāditam paścāt kevalam ambujaṃ smaret ॥
aiśāna-soma-diṅ-madhye catur-aśra-pure .atha vā ।
dvāra-śobhāgra-nirmukte rekhā-tritaya-bhūṣite ॥
tad antare .ardha-candrasthe kamale .aṣṭa-dalānvite ।
sāmrājye viniyuktaṃ yad vighnānām acyutena tat ॥

One may meditate on the pentad or nonad of deities, Dharma etc., until Ananta. Thereafter, one may meditate on the One lotus enveloped by sattva. [Then one worships Viṣvaksena] between the northeastern and the northern directions or in a square yantra. It lacks doors and flanges (typical of other square yantra-s), and [its periphery is] marked with triple lines. Inside it, stationed atop a lunar crescent, is a lotus with eight petals. [In it is stationed] he who is appointed as the overlord of obstacles by Acyuta himself.

The above rendering is faithful to that mentioned in the Pauṣkara, including some further details that are implicit in it and followed by mantravādin-s.
The central mantra of Viṣvaksena is that specified in saṃdhya-bhāṣā in the Lakṣmītantra and made explicit in its gloss (rhūṃ vauṃ).+++(5)+++
In actual practice, it is inscribed by sādhaka-s in the central position occupied by Viṣvaksena (see below).

There is also a strong conservation of the location for the worship of Viṣvaksena in different early Pāñcarātrika texts. For example, this is specified thus in the Lakṣṃī-tantra, chapter 38:

soma-śaṃkara-diṅ-madhye kha-sthitaṃ saṃsmaret prabhum ।
viṣvaksenam udārāṅgam āyāntaṃ gaganāntarāt ॥

One should meditate on the lord, stationed in the sky, between the northern and northeastern directions. Viṣvaksena of benefic body [is visualized] as coming from the sky.

A similar account is given by the Jayākhya Saṃhitā in its 13th chapter describing the maṇḍala worship of Viṣṇu:

tryambakottara-digbhyāṃ tu
madhyataḥ kha-sthitaṃ smaret ।
viṣvaksenaṃ dvijaśreṣṭha
āyāntaṃ gaganāntarāt ॥

Visualization

Pauṣkara

The visualization of Viṣvaksena (Pauṣkara, chapter 20):

iṣṭvā hṛt-puṇḍarīke tu
svāpekṣā-niṣkalātmakam ।
tam eva sakalatvena
yātaṃ dhyātvā yajed bahiḥ ॥
nava-dūrvāṅkurābhaṃ ca tvīṣat pītala-kānti-dhṛt
catur-daṃṣṭraṃ catur-bāhuṃ catur-muṣkaṃ catur-gatim॥
pūrṇāṅgaṃ kesari-skandhaṃ pṛthūras-sthala-rājitam ।
dakṣiṇā-varta-nimnena nābhi-randhreṇa śobhitam ॥
ājānu-bāhuṃ śrīmantaṃ piṅgalārcir-jaṭādharam ।
dravat kanaka-piṅgākṣa-cubukaṃ pṛthu-nāsikam॥
sita-dīrgha-nakha-śreṇi-śobhitaṃ kuṭila-bhruvam ।
muktā-vibhūṣitaṃ madhye mahāratnopa-saṃskṛtam॥
kuryāc ca dakṣiṇe pakṣe kṛta-śrīvatsa-maṅgalam ।
amāsitakyomaṇi(?) (…) tanmadhye kamalālayam ॥
dviguṇaṃ brahma-sūtraṃ syān nābheś cābhi-pradakṣiṇam ।
vistīrṇa-gaṇḍa-vadanaṃ bālendu-kuṭilopamaiḥ ॥
nava-kiṃśukāruṇābhair-lomaiḥ saṃpūrṇā-vigraham ।
śobhanena pralambena pṛthunā pronnatena ca ॥
māṇikya-kuṇḍalāḍhyena yuktaṃ śrotra-dvayena tu ।
mukuṭenonnatenaiva hārādyair upaśobhitam ॥
citra-kauśeya-vasanaṃ vicitra-sragvimaṇḍitam ।
pralaya-dvādaśāditya-sahasraguṇa-dīdhitim ॥
īṣad ūrdhve tathā tiryag vinipātita-locanam ।
kundendu-kānti-daśanaṃ kiñcid-vihasitānanam ॥
svabhāva-saumyam amalam māyā-krodhoparañjitam ।
savilāsa-calat-pādanyāsa-sthānaka-saṃsthitam॥
svenāntaḥ karaṇenaiva bhāvayantam param padam ।
aṅguṣṭhena kaniṣṭhāntam aṅgulais tu latātrayam ॥
nāmayitvonnatā caikā ghrāṇena viniyojitā ।
sad-vighna-bhīti-pradayā tv anayā mudrayā .anvitam ॥
rathāṅga-śaṅkha-hastaṃ ca lambamāna-gadādharam ।
śroṇī-taṭa-niviṣṭena sāvahelena pāṇinā ॥
itthaṃ rūpadharaṃ devam anekādbhūta-vikramam ।
karṇikā-madhyagaṃ tasya hṛd-ādyāmukhya-mantravat ॥

Having worshiped him in the heart-lotus, verily in his independent, undifferentiated form, visualizing him as having gone forth in his differentiated form, one may then worship him externally [visualizing him thus:] Having the complexion of newly-sprouted Durva grass tinted with a slight yellowish luster; having four fangs, four arms, four testes and four gaits;
with a full body, lion-shoulders and flaunting a broad torso, endowed with a navel cavity bearing a clockwise spiral whorl;
having arms reaching to his knees, opulent and bearing dread-locks with a tawny blaze; having eyes and chin like molten gold and with a broad muzzle;
with an array of white, long nails, and with curved brows; with a pearl-decked necklace decorated with a great gem in the middle.
He should be made to bear the auspicious Śrīvatsa on his right side. [—corrupt+lacuna—] in the midst of a lotus pond;
with a two-fold ritual thread wound clockwise around the navel; with broad cheeks and face; with a form covered completely covered with ruddy hair of the color fresh kiṃśuka flowers; endowed with a beautiful, broad, well-stretched, and tall [form];
with two ears joined to ornaments of ruby; ornamented with a tall crown, garlands and the like;
with eyes slightly upturned and cast obliquely; with teeth white as jasmine and the moon, and a face bearing a slight smile;
though pacific and mild by nature, he displays the tint of mock anger. He stands with one foot stepping forth in a playful manner.
He is seen as meditating upon the supreme state (Viṣṇu) as his inner consciousness.
Having bent three of his creeper-like fingers from the thumb to the little finger, holding one erect, he unites it with his nose (This mudra might indicate prāṇāyāma).
His other [hand] assumes the mudra of causing fear to the obstacles [faced] by the good. His hands hold a wheel, a conch and a mace hanging downwards; One of his arms rests on the side of the hip in a warning pose. One should worship the god with such a form with many a miraculous power in the midst of the pericarp [of the lotus maṇḍala].

Lakṣṃī-tantra

There are several parallels found in the much shorter description provided by the Lakṣṃī-tantra’s account of the daily Pāñcarātrika-homa-vidhi.
Here, the ritualist sets aside some of the cooked rice for the offering
and makes fire sacrifices to Viṣvaksena (Lakṣṃī-tantra, chapter 40):

prāg eva vibhajed annaṃ prāpaṇāt saṃpradānataḥ ।
tenānnena yajet samyag viṣvaksenaṃ caturbhujam ॥
maṇḍalāntam upānīya samāhūyāmbarāntarāt ।
navāmra-patra-sadṛśaṃ piṅga-bhrū-śmaśru-locanam ॥
pīta-vastraṃ catur-daṃṣṭraṃ sva-mudrādvitayānvitam ।
gadā-khaḍga-dharaṃ devam abhyarcya kramaśaḥ sudhīḥ ॥
sāṅga-mudrām athā darśya gatvā kuṇḍa-samīpataḥ ।
viṣvaksenas tato bhaktyā tarpaṇīyas tilākṣataiḥ ॥
vauṣaḍ antena mantreṇa dadyāt pūrṇāhutiṃ tataḥ ।
maṇḍale pūjayitvātha kuryāt tasya visarjanam ॥
svamantreṇa suraśreṣṭha kṣamasveti padaṃ vadan ।
mudrāṃ ca darśayet taṃ ca nabhasy utpatitaṃ smaret ॥
viṣvaksenārcanaṃ sarvam agādhe .ambuni nikṣipet ।
toyenāstra-prajaptena plāvayen maṇḍalaṃ ca tat ॥

The ritualist should partition a portion of cooked rice from the storage vessel (we render prāpaṇa as such based on the parallel version in the Jayākhya; see below) before offering it [to Viṣṇu]. With that rice, he should sacrifice to the four-armed Viṣvaksena.
Having brought him close from the sky, the intelligent ritualist should invoke and worship with the due procedure [Viṣvaksena] in the maṇḍala as having the complexion of a young mango leaf with tawny brows, mustache and eyes;
wearing a yellow garment, with four fangs, displaying his own mudra; holding a mace and a sword.
Having then displayed the mudra-s of the aṅga-s and having gone close to the fire altar, he should thereafter, with devotion, make quenching offerings of sesame seeds and parched rice.
Then, with the [Viṣvaksena]-mantra ending with a vauṣaṭ, he should offer the final oblation. Having worshiped him in the maṇḍala, he should then perform his sendoff,
o lord of the gods (Indra, to whom Lakṣṃī is revealing the tantra), with his own mantra (Viṣvaksena) ending in the phrase “pardon me”. He should then display the mudra-s and visualize him as flying away into the sky.
He should then discard the items used in the worship of Viṣvaksena in deep water. He then immerses the maṇḍala in water by muttering the astra incantation.

Jayākhya

A similar ritual is provided in the Jayākhya Saṃhitā, chapter 14:

tena bhāṇḍa-sthitenāpi samāhūyāmbarāntarāt ।
viṣvaksenaṃ yajed bhaktyā dhyātvā vai maṇḍalāntare ॥
catur-bhujam udārāṅgaṃ gadā-śaṅkha-dharaṃ vibhum ।
navāmra-patra-saṅkāśaṃ piṅgala-śmaśru-locanam ॥
pīta-vastraṃ catur-daṣṭraṃ sva-mudrādvitayānvitam ।
samabhyarcya kramātsāṅgaṃ mudrām asyātha darśayet ॥
gatvā kuṇḍa-samīpaṃ tu mantraṃ puṣpaiḥ prapūjya ca ।
bhasmanā .astrābhitaptena lalāṭe tilakaṃ śubham ॥
kṛtvā maṇḍalavat paścād upasaṃhṛtya cātmani ।
viṣvaksenas tato bhaktyā tarpaṇīyas tilākṣataiḥ ॥
vauṣaḍ antena mantreṇa dadyāt pūrṇāhutiṃ dvija ।
maṇḍale pūjayitvā .atha kuryāt tasya visarjanam ॥
svamantreṇa dvijaśreṣṭha kṣamasveti padena ca ।
mudrā-samanvitenātha nabhasy utpatitaṃ smaret ॥
pūrṇena kalaśenātha astra-japtena nārada ।
kṣīrāmbu-madhurājyena prāpayen maṇḍalaṃ tu tat ॥
tataḥ kuṇḍāt samutthāpya viṣvaksenaṃ yathā purā ।

Therianthropomorphy

A key point regarding Viṣvaksena’s iconography in the tāntrika texts is his apparently therianthropomorphic form.
While some Vaiṣṇava-s closer to our times have conflated his iconography on occasions with that of Vināyaka (see below), it is clear from the old Pāñcarātrika texts that this was not the case for Viṣvaksena — he is never called Gajavaktra in these texts.
Nevertheless, the above-cited saṃhitā-s are united in mentioning him as having four fangs suggestive of therocephaly.
This is made more concrete in his most detailed iconography presented in the Pauṣkara. There, several explicit descriptors are provided, such as lion-shouldered, having a broad muzzle, ruddy hair, tawny locks, and long nails/claws.
Taken together with him being four-fanged, it appears that the early Pāñcarātrika tantra-s conceived this god as having leonine aspects or being lion-faced.

Quasi-nandin

This therianthropomorphic form also suggests a thematic overlap with Nandin in the śaiva world, who was originally seen as being ape-headed.
Like Nandin, Viṣvaksena is seen as the chief of the Gaṇarājeśvara-s of Viṣṇu’s hosts (see below).

Puṣpadharā

While these texts do not specify the iconography of Viṣvaksena’s wife, Puṣpadharā (the medieval Śrīvaiṣṇava scholar Vedānta-deśika call her Sūtravatī), her iconography is briefly specified by the Pādma-saṃhitā as being similar to that of Śrī (Kriyāpāda, chapter 22):

devīṃ ca viṣvaksenasya
vāmapārśve pratiṣṭhitām ।
nāmnā puṣpadharāṃ kuryāt
kamalām iva lakṣitām ॥

Gaṇarājeśvara-s

The other Gaṇarājeśvara-s (Pauṣkara, chapter 20):

padmac-chadāntarasthāṃ ca tadā-karadyutiṃ vinā ।
kintv aṅgānāṃ ca sarvatra dhyānam uktaṃ sitādikam ॥
gajānano jayatseno harivaktro mahābalaḥ ।
kālaprakṛti saṃjñaśva caturthaḥ kamalodbhava ॥
gaṇa-rājeśvarā hyete catvāraś caṇḍavigrahāḥ ।
ājñā-pratīkṣakāś cāsya suśveta-camarodyatāḥ ॥
vināyakādayaś caiva vighneśa-pravarāstu ye ।
amīṣāṃ gaṇanāthānāṃ nityam-ājñānupālinām ॥
īśānādiṣu koṇeṣu padma-bāhyasthitān nyaset ।
vīkṣamāṇā vibhor vaktraṃ tat tulya sthānakā-sthitāḥ ॥
tadvat karāṅkitāḥ sarve kintu mudrā-vivarjitāḥ ।
dhyānam eṣāṃ pṛthag bhūtaṃ śarīram avadhāraya ॥
bhīmaṃ dvipendra-vadanaṃ catur-daṃṣṭraṃ trilocanam ।
kambu-grivaṃ catur-bāhuṃ pūrṇa-candrāyuta-dyutim ॥
hāra-nūpura-keyūra-mekhalādāma-maṇḍitam ।
nānā srag-gandha-vastrāḍhyam anaupamya-parākramam ॥
dhyāyed gajānanam ato jayatsenaṃ ca saṃsmaret ।
mahat-turaṅga-vadanaṃ padmarāgācala-prabham ॥
dravac cāmīkarākṣaṃ ca anekādbhuta-vikramam ।
harivaktram ato dhyāyet saṭāc churita-mastakam ॥
niṣṭapta-kanaka-prakhyaṃ ghora-gharghara-nikhanam ।
mṛga-rāḍ-vadanaṃ vipra kalpāntānila-veginam ॥
kālaprakṛti-nāmānaṃ bhāvayed añjanādrivat ।
daṃṣṭrā-karāla-vadanaṃ piṅgala-śmaśru-locanam ॥
jhaṣa-kuṇḍalinaṃ raudraṃ mīnavan nimna-nāsikam ।
gaṇa-rājeśvarā hyete mahā-puruṣa-lakṣaṇaiḥ ॥
saṃyuktāś cākhilair vipra tv āpādāt kandharāv adhi ।
yat kiñcin maṇḍanaṃ vastu tadādyoktaṃ smaret triṣu ॥
eteṣām arcanaṃ kuryāt svanāmnā praṇavādinā ।
namontenābja-saṃbhūta nānā-siddhi-phalāptaye ॥

Within the bounds of the lotus [maṇḍala] and without the [central] radiance of rays (this part is unclear to us, but it apparently refers to the petals of the yantra outside the central region where the radiance of Viṣvaksena is situated) but with all limbs [aṅga mantra-s] the meditation of the retinue gods is specified, colored white etc (mantravādin-s state that these are white, red, yellow and black).
Gajānana, Jayatsena, Harivaktra and Kālaprakṛti of great might, these together are known as the tetrad, o lotus-born one. These four king-lords of the gaṇa-s [of Viṣṇu] of fierce forms attend to [Viṣvaksena’s] orders, with good white yak-tail fly-whisks held aloft.
Then there are Vināyaka, etc., those who have Vighneśa as their chief, ever obedient to the orders of those lords of the gaṇa-s (The aforesaid tetrad of Gaṇarājeśvara-s).
These should be placed in the Northwest etc corners (i.e., at the interstitial directions) outside the lotus.
They should look towards their [respective gaṇa] lord, adopting a stance equivalent to them. Their hands are equipped with the same implements, but they do not display any mudra. Please pay attention [now] to the visualization of the embodied forms assumed by each [Gaṇarājeśvara].
With the face of a terrible elephant-lord, with four tusks and three eyes, having a neck [smooth as a] shell, with four arms and the radiance of a 10,000 full moons;
ornamented with garlands, anklets, armlets, a girdle and a necklace; decorated with various garlands, perfumes and vestures, and having unequaled valor;
thus, one should meditate on Gajānana.
Jayatsena should be visualized with a great horse-face, the radiance of a ruby mountain,
with eyes like molten gold, endowed with many miraculous powers. Then one meditates on Harivaktra with a head strewn with manes,
resembling heated gold and roaring like a terrible musical instrument (gharghara is an old Indo-Aryan musical instrument accompanying Vedic recitations and singing). O vipra, he has the face of the kings of the animals and the velocity of the wind at the end of the kalpa.
He, Kālaprakṛti by name, should be visualized as [resembling] a mountain of collyrium; with a terrifying face displaying fangs; with tawny mustache and eyes;
wearing shark-earrings, fierce and having a fish-like deep snout. O vipra, all these king-lords of the gaṇa-s possess all the marks of the great persons from the feet to their necks.
Whatever item of ornamentation was described for the first (Gajavaktra) should also be visualized for the [other] three.
O lotus-born one, the worship of all these should be performed with their respective names starting with the praṇava and ending in ‘namaḥ’ for the attainment of various siddhi-s.

shaiva-mapping

There are multiple remarkable features regarding these Gaṇarājeśvara-s:

1. Their names indicate a clear mapping onto their śaiva counterparts.
Gajavaktra (Elephant-faced)= Gaṇeśa;
Jayatsena (Conquering Army)= Skanda; Harivaktra (Lion-faced)= Haribhadra/Vīrabhadra;
Kālaprakṛti= Mahākāla.
In terms of iconography, that of Gajavaktra is transparently equivalent to that of Gaṇeśa. While the name of Jayatsena is an obvious match for Skanda,
his hippocephalous morphology is a stark deviation from that of the latter
and appears to be an attempt to capture some of the preexisting, ancient Vaiṣṇava iconography of Hayagrīva.
While the later iconography of Vīrabhadra lost the leonine visage,
that idiosyncrasy mentioned in the early texts (Haribhadra; e.g., the Proto-Skandapurāṇa) persisted in the classic Rudra-parivāra icons from Nepal.
As for Kālaprakṛti, he retains, in the least, the complexion of Mahākāla.

Given that these deities have deep roots in the śaiva tradition,
unlike the sudden appearance of their counterparts in the Vaiṣṇava tradition,
one may posit that they were pantheonic duplications to mirror their counterparts in the former tradition.

2. As noted above,
in most old saṃhitā-s Viṣvaksena is presented as iconographically distinct from Gaṇeśa.
Viṣvaksena shares the function of the remover of obstacles with Gaṇeśa.
Nevertheless, multiple Vaiṣṇava tantra-s emphasize his distinctness from the latter
and provide separate accounts of the worship of each of them (e.g., Jayākhya, Pauṣkara, Lakśmī). In the Pādma-saṃhitā, his iconography is provided thus (Kriyāpāda, chapter 22):

viṣvaksenaṃ caturbāhuṃ
śyāma-varṇaṃ kirīṭinam ।
lambodaraṃ ca mukhyena
kareṇābhaya-dhāriṇam ॥

Thus, he shares the lambodara feature with Vināyaka;
however, even here, he is not described as Gajavaktra and the iconography of Vināyaka is expounded separately from him:

gajānanaṃ catur-bāhuṃ
lambakuṣiṃ sitaprabham ।
karaṇḍikā-mukuṭinaṃ
lamba-yajñopavītinam ॥

These again point to pantheonic duplication rather than a simple replacement of Vināyaka by Viṣvaksena. The presentation of Viṣvaksena in the midst of 4 Vināyaka-s in the Pauṣkara
mirrors the depiction of Skanda in the midst of the same in the old Kaumāra tantra, the Ṣaṇmukha-kalpa.
Further, as the commander of Viṣṇu’s hosts, and in the very form of his name (whose army is everywhere),
Viṣvaksena takes on certain features of Kumāra.

3. The account of the 4 Vināyaka-s in the Pauṣkara has some unclear points.
First, all their names are not specified in this text.
Practicing mantravādin-s give them as
Vināyaka, Vighneśa, Pravara and Gaṇanātha.
These four names are derived from the above text, but they are not used in that sense in the text.
Second, they are said to be stationed outside the lotus of the yantra.
Given that the lotus has 8 petals, with Viṣvaksena in the pericarp, and the Gaṇarājeśvara-s in the 4 petals of the cardinal directions, we are still left with 4 more petals. Some mantravādin-s logically place the 4 Vināyaka-s in those petals contrary to the account in the text.+++(4)+++

Thus, the convergence between the retinues of the Rudra and Viṣṇu in the Tantric texts
presents some of the same features seen more broadly in the course of the evolution of natural religions,
especially the Indo-European religion.
While we see strong ritual-category convergence (Nirmālya-devatā-s),
their nature in terms of divine functionality shows a more diffuse overlap with the deities from the pantheons of other sects.