Seminar| Institute of Mathematical Sciences
Time：Wednesday, August 17th, 2022, 15:00-16:00
Location：Tecent Meeting
Speaker: Toshiaki Shoji, Tongji University
Abstract: Let U be the quantum group associated to a Kac-Moody algebra of symmetric type, and U_1 the quantum group obtained from an admissible diagram automorphism s on U. Let U^-, U_1^- be the negative part of U, U_1, respectively. Lusztig constructed the canonical basis B of U^- , and the canonical signed basis B'_1 of U_1^-, by using the geometric theory of quivers. Then he constructed the canonical basis B_1 of U_1^- from B'_1 by using Kashiwara's theory of crystals, and obtained the natural bijection between B^s and B_1, where B^s is the set of s-fixed elements in B. In this talk, we take a different approach for this problem. Assuming the existence of the canonical basis B of U^-, we construct the canonical signed basis B'_1 of U_1^- , and the bijection between B^s and B'_1, up to sign, in an elementary way. In the case where the order of s is odd, we can construct the canonical basis B_1, and the bijection between B^s and B_1. This is a joint work with Z. Zhou and Y. Ma.
Link: https://meeting.tencent.com/dm/CeacAtNdhzgU
Room Number: 902-181-314