Affine Laumon space and contragredient dual Verma module of U_q(\widehat\mathfrakgl_n)

2024/02/13 by Che Shen, Shen, Che
Mathematics · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2402.08613

Abstract

We study the action of the quantum group U_q(\widehat\mathfrakgl_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\mathfrakgl_n), improving earlier results of Braverman-Finkelberg and Neguţ. The proof uses a variant of stable envelopes first introduced by Maulik-Okounkov in the study of Nakajima quiver varieties.

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