Notes on Chevalley Groups and Root Category IV: Iwasawa Decomposition and Total Positivity

2026/07/26 by Buyan Li
#math.RT

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Abstract

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 positive submonoid of the Chevalley group.

Citations

• Notes on Chevalley Groups and Root Category II: Compact Lie Groups and Representations
• Notes on Chevalley Groups and Root Category I
• Total positivity in reductive groups, II

Related

• Notes on Chevalley Groups and Root Category I
• On the construction of Chevalley Supergroups
• Chevalley operations on TNN Grassmannians
• Cartan-Iwahori-Matsumoto decompositions for reductive groups
• From Weyl groups to semisimple groups