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arXiv · 2402.08613

Affine Laumon space and contragredient dual Verma module of $U_q(\widehat{\mathfrak{gl}}_n)$

Che Shen
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Abstract

We study the action of the quantum group $U_q(\widehat{\mathfrak{gl}}_n)$ on the equivariant K-theory of affine Laumon spaces. We show that, at any lowest weight away from the critical level, this can be identified with the contragredient dual Verma module of $U_q(\widehat{\mathfrak{gl}}_n)$, improving earlier results of Braverman-Finkelberg and Negu\c{t}. The proof uses a variant of stable envelopes first introduced by Maulik-Okounkov in the study of Nakajima quiver varieties.

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BibTeXRIS

Che Shen. 2024-02-13. Affine Laumon space and contragredient dual Verma module of $U_q(\widehat{\mathfrak{gl}}_n)$. https://arxiv.org/abs/2402.08613

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