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2020年5月22日(金) 15:00~16:30
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藤田遼氏(京都大学理学研究科)
Singularities of R-matrices, graded quiver varieties and generalized quantum affine Schur-Weyl duality
The R-matrices are realized as intertwining operators between tensor products of two finite-dimensional simple modules of the quantum affine algebras. They can be seen as matrix-valued rational functions in spectral parameters, whose singularities strongly reflect the structure of tensor product modules. In this talk, we present a simple unified formula expressing the denominators of the R-matrices between the fundamental modules of type ADE and explain its relation to the representation theory of the Dynkin quivers / the geometry of Nakajima’s graded quiver varieties. As an application, 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. Such a geometric interpretation sometimes provides an efficient way to understand the monoidal structure of the module category of the quantum affine algebras.