Graded quiver varieties and singularities of normalized R-matrices for fundamental modules - Sorbonne Université
Journal Articles Selecta Mathematica (New Series) Year : 2022

Graded quiver varieties and singularities of normalized R-matrices for fundamental modules

Abstract

We present a simple unified formula expressing the denominators of the normalized R-matrices between the fundamental modules over the quantum loop algebras of type ADE. It has an interpretation in terms of representations of Dynkin quivers and can be proved in a unified way using geometry of the graded quiver varieties. As a by-product, we obtain a geometric interpretation of Kang-Kashiwara-Kim's generalized quantum affine Schur-Weyl duality functor when it arises from a family of the fundamental modules. We also study several cases when the graded quiver varieties are isomorphic to unions of the graded nilpotent orbits of type A.
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Dates and versions

hal-03556993 , version 1 (04-02-2022)

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Ryo Fujita. Graded quiver varieties and singularities of normalized R-matrices for fundamental modules. Selecta Mathematica (New Series), 2022, 28 (1), ⟨10.1007/s00029-021-00715-5⟩. ⟨hal-03556993⟩
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