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

Fujita, Ryo 京都大学 DOI:10.1007/s00029-021-00715-5

2022.02

概要

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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(R. Fujita) Research Institute for Mathematical Sciences, Kyoto University, Oiwake´matiques de JussieuKitashirakawa, Sakyo, Kyoto, 606-8502, Japan & Institut de Mathe

´ de Paris, F-75013, Paris, France

Paris Rive Gauche, Universite

Email address: rfujita@kurims.kyoto-u.ac.jp

...

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