Geodesic
A Steinberg Cross Section for Non-Connected Affine Kac—Moody Groups
Canadian journal of mathematics, Tome 58 (2006) no. 3, pp. 625-642

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2006-026-7
Mots-clés : 22E67 
Mohrdieck, Stephan. A Steinberg Cross Section for Non-Connected Affine Kac—Moody Groups. Canadian journal of mathematics, Tome 58 (2006) no. 3, pp. 625-642. doi: 10.4153/CJM-2006-026-7
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