Generalizations Of The Cartan And Iwasawa Decompositions For SL$_2(k)$

zbMATH Open1377.20034arXiv1410.3439MaRDI QIDQ2977477

Amanda K. Sutherland

Publication date: 18 April 2017

Abstract: The Cartan and Iwasawa decompositions of real reductive Lie groups play a fundamental role in the representation theory of the groups and their corresponding symmetric spaces. These decompositions are defined by an involution with a compact fixed-point group, called a Cartan involution. For an arbitrary involution, one can consider similar decompositions. We offer a generalization of the Cartan and Iwasawa decompositions for algebraic groups defined over an arbitrary field $k$ and a general involution.

Full work available at URL: https://arxiv.org/abs/1410.3439

zbMATH Keywords

Cartan decompositionIwasawa decompositiongeneralized symmetric spacesreal reductive Lie groups

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) General properties and structure of real Lie groups (22E15)

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