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A Steinberg Cross Section for Non–Connected Affine Kac—Moody Groups
- Source :
- Canadian Journal of Mathematics. 58:625-642
- Publication Year :
- 2006
- Publisher :
- Canadian Mathematical Society, 2006.
-
Abstract
- 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 𝕔*-action.
- Subjects :
- Connected component
Pure mathematics
General Mathematics
010102 general mathematics
Coxeter group
01 natural sciences
Algebra
Mathematics::Group Theory
0103 physical sciences
010307 mathematical physics
Affine transformation
0101 mathematics
Mathematics::Representation Theory
Crucial point
Coxeter element
Quotient
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 58
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........02b9753c8c063740a197feb9ed3f5227