* 시간: 7월17일 3:00~4:00,
7월18일 오전 11:00~12:00, 오후 1:30~2:30, 3:00~4:00

In this lecture, I will explain the generalized quantum Schur-Weyl duality functor using quiver Hecke algebras given by Kang, Kashiwara and Kim. This functor is a vast generalization of quantum Schur-Weyl duality between module categories of the affine Hecke algebra of type A and the quantum affine algebras of type A. Let $$extract_itex$$U_q’(g)$$/extract_itex$$ be a quantum affine algebra, and let $$extract_itex$$\{ V_j \}_{j \in J}$$/extract_itex$$ be a family of quasi-good $$extract_itex$$U_q’(g)$$/extract_itex$$-modules. The generalized quantum Schur-Weyl duality provides a procedure to make a symmetric quiver Hecke algebra $$extract_itex$$R^J$$/extract_itex$$ from the R-matrices among $$extract_itex$$\{ V_j \}_{j \in J}$$/extract_itex$$ and to construct a monoidal functor F with good properties from the finite-dimensional $$extract_itex$$R^J$$/extract_itex$$-module category to the finite-dimensional $$extract_itex$$U_q’(g)$$/extract_itex$$-module category. This is a 4 hour lecture with the following content: Categorification using quiver Hecke algebras Quiver Hecke algebra of type $$extract_itex$$A$$/extract_itex$$ R-matrices for quantum affine algebras Generalized Schur-Weyl duality.