Seminar

Speaker:
10:00-10:50 am: Buyan Li, Tsinghua University, title: "Root Category and Simple Groups of Lie Type"

Abstract:
Ringel used the representation theory of finite-type hereditary algebra and Hall polynomials to obtain the positive part of the simple Lie algebra.Peng and Xiao generalized Ringel's result to root category and obtained the whole Lie algebra. Based on their constructions, we construct the compact real form of the complex semisimple Lie algebra, and the Chevalley group of the root category, as well as its maximal compact subgroup. On the other hand, Lusztig used the modified quantum group and its canonical basis to obtain the reductive group and its coordinate ring O. By combining these, we explore how the classical theory of compact Lie groups, such as Peter-Weyl theorem and Plancherel theorem, can be recovered completely.This talk is based on a joint work with Prof. Jie Xiao.

11:00-11:50 am: Yixin Lan, MPI Bonn, title: "From Lusztig's canonical bases to Nakajima quiver varieties“
Abstract:
In this talk, I will use a geometric tool to build a morphism from the canonical bases of integrable modules of quantum groups to the top Borel-Moore homology groups of Nakajima’s quiver varieties. As an application, one can give a new proof of Nakajima’s conjecture on the canonical isomorphism of tensor product varieties. This is a joint wok with Jiepeng Fang.

The next SWAG meeting takes place on 

Friday, November 28, 2025
at 10:00 am - 18:00 pm
at the University of Ulm, Department of Mathematics, Helmholtzstr. 16, 89081 Ulm

URTAGS

ILIAS course A'n'G