Date | Jul 18, 2019 |
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Speaker | 박의용 |

Dept. | 서울시립대학교 |

Room | 129-301 |

Time | 11:00-16:00 |

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

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