On convexity and the Iwasawa decomposition of split real and complex Kac-Moody groups

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Bibliographic Details
Main Authors:	Zellhofer, Paul, Köhl, Ralf
Format:	Preprint
Published:	2023
Subjects:	Representation Theory Group Theory 20G02
Online Access:	Acceder al recurso
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author	Zellhofer, Paul Köhl, Ralf
author_facet	Zellhofer, Paul Köhl, Ralf
contents	We prove an analogue of Kostant's convexity theorem for split real and complex Kac-Moody groups associated to free and cofree root data. The result can be seen as a first step towards describing the multiplication map in a Kac-Moody group in terms of Iwasawa coordinates. Our method involves a detailed analysis of the geometry of Weyl group orbits in the Cartan subalgebra of a real Kac-Moody algebra. It provides an alternative proof of Kostant convexity for semisimple Lie groups and also generalizes a linear analogue of Kostant's theorem for Kac-Moody algebras that has been established by Kac and Peterson in 1984.
format	Preprint
id	arxiv_https___arxiv_org_abs_2312_02584
institution	arXiv
publishDate	2023
record_format	arxiv
spellingShingle	On convexity and the Iwasawa decomposition of split real and complex Kac-Moody groups Zellhofer, Paul Köhl, Ralf Representation Theory Group Theory 20G02 We prove an analogue of Kostant's convexity theorem for split real and complex Kac-Moody groups associated to free and cofree root data. The result can be seen as a first step towards describing the multiplication map in a Kac-Moody group in terms of Iwasawa coordinates. Our method involves a detailed analysis of the geometry of Weyl group orbits in the Cartan subalgebra of a real Kac-Moody algebra. It provides an alternative proof of Kostant convexity for semisimple Lie groups and also generalizes a linear analogue of Kostant's theorem for Kac-Moody algebras that has been established by Kac and Peterson in 1984.
title	On convexity and the Iwasawa decomposition of split real and complex Kac-Moody groups
topic	Representation Theory Group Theory 20G02
url	https://arxiv.org/abs/2312.02584

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