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

• Ryo Fujita ^[1]
  1. [1] Kyoto University, Japón; Université de Paris, Francia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 28, Nº. 1, 2022
• Idioma: inglés
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• Resumen

  • 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 {\mathsf {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 \mathsf {A} .