Affine super Yangians and rectangular W-superalgebras

Abstract

Motivated by the Alday-Gaiotto-Tachikawa (AGT) conjecture, we construct a homomorphism from the affine super Yangian [Formula: see text] to the universal enveloping algebra of the rectangular W-superalgebra [Formula: see text] for all m ≠ n, m, n ≥ 2 or m ≥ 3, n = 0. Furthermore, we show that the image of this homomorphism is dense, provided that k + ( m − n)( l − 1) ≠ 0.