Affine Yangian action on the Fock space

Abstract

The localized equivariant homology of the quiver variety of type $A_{N-1}^{(1)}$ can be identified with the level one Fock space by assigning a normalized torus fixed point basis to certain symmetric functions, Jack(${\mathfrak{gl}}_N$) symmetric functions introduced by Uglov. We show that this correspondence is compatible with actions of two algebras, the Yangian for ${\mathfrak{sl}}_N$ and the affine Lie algebra ${\widehat{\mathfrak{sl}}}_N$, on both sides. Consequently we obtain affine Yangian action on the Fock space.

v2, 46pages, several errors are corrected. In particular, a part of the defining relations of the affine Yangian was wrong in the first version

References in corpus (1)

• Bases in coset conformal field theory from AGT correspondence and Macdonald polynomials at the roots of unity

Cited by in corpus (5)

• Coproduct for the Yangian of an affine Kac-Moody algebra
• Homomorphisms between different quantum toroidal and affine Yangian algebras
• Braid Group Action on Affine Yangian
• Elliptic Stable Envelopes and Finite-dimensional Representations of Elliptic Quantum Group
• Higher level Fock spaces and affine Yangian