3 papers
math.RT2026
Notes on Chevalley Groups and Root Category III: the Region of Total Positivity
Buyan Li, Jie Xiao
In [4], we use the root categories to realize Chevalley groups. Lusztig's theory of total positivity for reductive groups can be naturally applied to Chevalley groups. In this pape…
math.RT2025
Notes on Chevalley Groups and Root Category II: Compact Lie Groups and Representations
Buyan Li, Jie Xiao
This paper is a continuation of [5]. Using the root categories, we define the compact real forms of the complex semisimple Lie algebras, and maximal compact subgroups of the Cheval…
math.RT2025
Notes on Chevalley Groups and Root Category I
Buyan Li, Jie Xiao
Based on the construction of simple Lie algebras via root category and following Chevalley's results, we construct Chevalley groups from the root category. Then we prove the Bruhat…