A Steinberg Cross Section for Non-Connected Affine Kac--Moody Groups
Printed: Jun 2006
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 $\Cst$-action.
22E67 - Loop groups and related constructions, group-theoretic treatment [See also 58D05]