BIMSA > Automorphic representations and Harmonic analysis Automorphic representations and Harmonic analysis Root category and total positivity
Root category and total positivity
Organizers
Taiwang Deng , Sergei Oblezin , Dongming She
Speaker
Buyan Li
Time
Thursday, November 5, 2026 1:30 PM - 2:30 PM
Venue
A3-4-301
Online
Zoom 435 529 7909 (BIMSA)
Abstract
We use root categories to realize Chevalley groups and their maximal compact subgroups. Moreover, we obtain the Cartan and Iwasawa decomposition theorems. On the other hand, Lusztig's theory of total positivity for reductive groups can be naturally applied to Chevalley groups. In this talk, I will explicitly determine regions of Extra close brace or missing open brace, for describing the size of monoids of totally positive elements, with respect to the root subgroups corresponding to the indecomposable objects in the root category. Then I will talk about the Iwasawa decomposition for totally positive monoids. This is based on joint works with Professor Jie Xiao.