Bhagavad-Gita: Chapter 10, Verse 37

Rudra Vaisnava Sampradaya:

Visnuswami

Sridhara Swami's Commentary

Of the Vrishnis or His apparent lineage, Lord Krishna's vibhuti or divine, transcendental opulence is Vasudeva which means the son of Vasudeva. It would not be acceptable for Lord Krishna to be naming Himself because He is describing His vibhuti and so the only other son of Vasudeva is Balarama who is Lord Krishna's first and foremost expansion and who expands as all the other incarnations with the exception of Narayana the ruler of all the spiritual planets in the spiritual realm of Vaikuntha who is Lord Krishna's direct expansion. Of holy sages or those who are knowledgeable of all the Vedic scriptures Lord Krishna's vibhuti is Vyasadeva who divided the one Veda into four, wrote the Puranas and Brahma Sutras and compiled the historical treatise Mahabharata. Of exalted seers or those who are omniscient His vibhuti is Usanah the son of Brgu who is known as Sukracarya the guru of the asuras or those born in demonic lines.

Brahma Vaisnava Sampradaya:

Madhvacarya

Madhvacarya's Commentary

Enveloping everything or containing all, abiding in all and the goal of all Lord Krishna is known as Vasu, Being the God of all gods He is known as deva. Thus He is Vasudeva and a vibhuti or divine, transcendental opulence of Lord Krishna. The Moksa Dharma scripture states: Enveloping all creation He illuminates it just like the rays of the sun as the indwelling monitor within all living entities, He is therefore known as Vasudeva. Being especially in all things as the best of them, His vibhuti is Vyasa. The Agniveshya section states: He is Vyasa. Vy means the best. He is above, He is below, He is in the east, He is in the west, He is in the north and He is in the south. Whatever we see or hear in any direction externally or internally in all dimensions is already established by the Supreme Lord.

Sri Vaisnava Sampradaya:

Ramanuja

Ramanuja's Commentary

The Vrishni lineage descends from King Yayati and Queen Devayani from which Vasudeva is the sixth generation of descendants. Lord Krishna's vibhuti or divine, transcendental opulence cannot be referring to Himself as the son of Vasudeva because He is describing His vibhuti. The only other son of Vasudeva is Balarama who is Lord Krishna's first expansion and manifests every incarnation including Vishnu. So Balarama is the vibhuti referred to here. Of sages or those who have realised the ultimate truth His vibhuti is Vedavyasa. Kavayah are those seers who are omniscient.

Kumara Vaisnava Sampradaya:

Nimbaditya

Kesava Kasmiri's Commentary

Among the descendants of the Vrishni lineage Lord Krishna's vibhuti or divine, transcendental opulence is the son of Vasudeva. As Lord Krishna is describing His vibhuti it is not logical that He would be would be referring to Himself. The only other son of Vasudeva is Balarama who is the first expansion of Lord Krishna and the direct source of all other avataras or incarnations including Rama and Vishnu. So Lord Krishna's vibhuti as the son of Vasudeva is the all powerful Balarama. Lord Krishna declares that among the Pandavas His vibhuti is Arjuna and among self-realised sages His vibhuti is Vedavyasa and among seers or those who are omniscient His vibhuti is Usanah better known as Sukracarya, the preceptor of those born in demoniac lines.