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

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dc.creatorMohrdieck, Stephan
dc.date2004-01-16
dc.date.accessioned2026-07-07T05:04:37Z
dc.date.available2026-07-07T05:04:37Z
dc.descriptionWe generalise the concept of a Steinberg cross-section to non-connected Kac-Moody group. As in the connected case, which was treated by G. Brüchert, a quotient map w.r.t the conjugacy action exists only on a certain submonoid of the Kac-Moody group. Non-connected Kac-Moody groups appear naturally as semidirect product of \C^* with a central extension of loop groups LG, where the underlying simple group G is no longer simply connected and might even be non-connected. In contrast to the connected case, the understanding of central extensions of non-connected loop groups is a rather complicated issue. Following the approach of V. Toledano Laredo, who dealt with the case of automorphisms coming from the fundamental group pi_1(G), we classify all of these central extensions for cyclic component group of LG. Then, we define the quotient map w.r.t conjugacy action. Furthermore, we construct the cross-section in every connected component of LG and show that, due the one-dimensional centre, it carries a natural \C^*-action which does not exist in the finite dimensional case.
dc.description37 pages, 5 tables
dc.identifierhttps://arxiv.org/abs/math/0401203
dc.identifierhttp://arxiv.org/abs/math/0401203
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/69874
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.subject22E67
dc.titleA Steinberg Cross-Section for Non-Connected Affine Kac-Moody Groups
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