Induced conjugacy classes, prehomogeneous varieties, and canonical parabolic subgroups

2012/06/14 by Werner Hoffmann, Hoffmann, Werner
Mathematics · #14L30 #20G15 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:14L30 #msc:20G15

paper · pdf · doi:10.48550/arxiv.1206.3068

New proofs given for the results on induction of conjugacy classes in section 1

arxiv created 2013/01/04 · arxiv updated 2013/01/07

Abstract

We extend the notion of induced conjugacy classes in reductive groups, introduced by Lusztig and Spaltenstein for unipotent classes, to arbitrary classes. We study properties of equivariant fibrations of prehomogeneous affine spaces, especially the existence of relative invariants. We also detect prehomogeneous affine spaces as subquotients of canonical parabolic subgroups attached to elements of reductive groups in the sense of Jacobson-Morozov. These results are prerequisites for making the geometric expansion of the Arthur-Selberg trace formula more explicit.

Related

• The trace formula and prehomogeneous vector spaces
• From conjugacy classes in the Weyl group to unipotent classes
• From conjugacy classes in the Weyl group to unipotent classes, II
• From unipotent classes to conjugacy classes in the Weyl group
• Conjugacy classes in parabolic subgroups of general linear groups