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 the Dynkin quivers and can be proved in a unified way using the geometry of 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 fundamental modules. We also study several cases when the graded quiver varieties are isomorphic to the graded nilpotent orbits of type A.

37 pages, v4: minor revision, to appear in Sel. Math. New Ser

References in corpus (2)

• Categorical relations between Langlands dual quantum affine algebras: Exceptional cases
• Geometric realization of Dynkin quiver type quantum affine Schur-Weyl duality

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