Krishna in Sri Vaishnavism
Kṛṣṇa (Sanskrit: कृष्ण — 'the dark one' or 'the all-attractive') is the most celebrated of the Lord's vibhava-avatāras — the form in which Śrīman Nārāyaṇa revealed the Bhagavad Gīṭā and displayed the summit of divine play (Lilā). While all avatāras are equally Brahman, Kṛṣṇa is often considered the pūrṇa-avatāra — the 'complete' avatāra in which all divine qualities are most fully expressed.
The Avatāra of Love
In the Śrī Vaiṣṇava tradition, Kṛṣṇa's most celebrated quality is His playful intimacy (mādhurya) with His devotees. The gopī (cowherd girl) stories of Vṛndāvana — their love, longing, and union with Kṛṣṇa — are the supreme expression of bhakti in its most intimate, complete form. The Āzhvārs frequently employ the gopī motif to express their own devotional longing.
The Gīṭā Teacher
Kṛṣṇa's role as Arjuna's charioteer and the revealer of the Bhagavad Gīṭā is central to Śrī Vaiṣṇava theology — the Gīṭā contains the Lord's most direct teaching on dharma, karma, jñāna, bhakti, and ultimately prapatti (in the carama-śloka). Rāmānuja's Gīṭā Bhāṣyam interprets Kṛṣṇa's teachings through Viśiṣṭādvaita.
Āṇḍāḷ's Kṛṣṇa
Āṇḍāḷ's Tiruppāvai and Nāciyār Tirumozhhi are both addressed to Kṛṣṇa — She approaches Him as the divine lover/husband. Her fervent, intimate devotion to Kṛṣṇa is the most celebrated example of mādhurya-bhakti in the Tamil tradition.