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arXiv · 2210.16138

Gelfand--Graev functor and quantum affine Schur--Weyl duality

Fan Gao·Nadya Gurevich·Edmund Karasiewicz
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Abstract

We explicate relations among the Gelfand--Graev modules for central covers, the Euler--Poincaré polynomial of the Arnold--Brieskorn manifold, and the quantum affine Schur--Weyl duality. These three objects and their relations are dictated by a permutation representation of the Weyl group. Specifically, our main result shows that for certain covers of $\mathrm{GL}(r)$ the Gelfand--Graev functor is related to quantum affine Schur--Weyl duality. Consequently, the commuting algebra of the Iwahori-fixed part of the Gelfand--Graev representation is the quotient of a quantum group.

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BibTeXRIS

Fan Gao, Nadya Gurevich, Edmund Karasiewicz. 2023-04-04. Gelfand--Graev functor and quantum affine Schur--Weyl duality. https://arxiv.org/abs/2210.16138

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