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arXiv · 1506.01246

Affine Yangian action on the Fock space

Ryosuke Kodera
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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 $\hat{\mathfrak{sl}}_N$, on both sides. Consequently we obtain affine Yangian action on the Fock space.

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Ryosuke Kodera. 2015-06-03. Affine Yangian action on the Fock space. https://arxiv.org/abs/1506.01246

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