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

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arxiv 2402.08613 v3 pith:X7P3KHCI submitted 2024-02-13 math.RT

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classification math.RT
keywords mathfrakwidehataffinecontragredientduallaumonmoduleverma
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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 highest 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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Relative Quasimaps and Tilting Module of $U(\mathfrak{gl}_n)$

    math.AG 2025-09 conditional novelty 8.0 of 10

    The equivariant cohomology of the moduli space of relative quasimaps to the flag variety carries a U(gl_n)-action whose specialized summand is, up to a known category equivalence, a tilting module.

  2. Athinization of irreducible $\widehat{\mathfrak{gl}}_n$-modules with dominant highest weights

    math.RT 2026-07 accept novelty 6.5 of 10

    Irreducible affine gl_n-modules with dominant highest weights become thin Yangian modules via restriction of periodic Gelfand-Tsetlin patterns to a permitted subset.

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