GTM seminar

Speaker: Ryo Fujita (Kavli IPMU)
Title: Singularities of R-matrices, graded quiver varieties, and generalized quantum affine Schur-Weyl duality
Date (JST): Thu, Aug 27, 2020, 15:30 - 17:00
Place: Zoom
Related File: 2559.pdf
Abstract: R-matrices are realized as intertwining operators between tensor products of finite-dimensional modules over the quantum loop algebras. They can be seen as matrix-valued rational functions in spectral parameters satisfying the Yang-Baxter equation and their singularities strongly reflect the structure of tensor product modules. In this talk, we explain the relationship among the singularities of R-matrices for the fundamental modules of type ADE, the representation theory of Dynkin quivers, and the geometry of Nakajima's graded quiver varieties. As a by-product, we obtain a geometric interpretation of the generalized quantum affine Schur-Weyl duality introduced by Kang-Kashiwara-Kim, which enables us to understand the representation theory of quantum loop algebras through that of quiver Hecke algebras.