4 papers
Notes on Chevalley Groups and Root Category IV: Iwasawa Decomposition and Total Positivity
Buyan Li
In this paper, we study the Cartan decomposition and Iwasawa decomposition of the Chevalley group from the root category. Then we investigate the Iwasawa decomposition for totally…
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…
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…
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…