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A Steinberg Cross Section for Non-Connected Affine Kac—Moody Groups

Published online by Cambridge University Press:  20 November 2018

Stephan Mohrdieck
Stephan Mohrdieck*
Affiliation:
Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg e-mail: stephan.mohrdieck@math.uni-hamburg.de
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Abstract

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In this paper we generalise the concept of a Steinberg cross section to non-connected affine Kac–Moody groups. This Steinberg cross section is a section to the restriction of the adjoint quotient map to a given exterior connected component of the affine Kac–Moody group. (The adjoint quotient is only defined on a certain submonoid of the entire group, however, the intersection of this submonoid with each connected component is non-void.) The image of the Steinberg cross section consists of a “twisted Coxeter cell”, a transversal slice to a twisted Coxeter element. A crucial point in the proof of the main result is that the image of the cross section can be endowed with a ${{\mathbb{C}}^{*}}$-action.

Keywords

22E67
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 3 , 01 June 2006 , pp. 625 - 642
Copyright
Copyright © Canadian Mathematical Society 2006

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