Thu, 30 Oct 2014
14:00 -
16:00
L4
Transversal slices to conjugacy classes in algebraic groups and Lustig's partition.
Alexey Sevastyanov
(The University of Aberdeen)
Abstract
I shall show that for every conjugacy class O in a connected semisimple algebraic group G over an algebraically closed field of characteristic good for G one can find a special transversal slice S to the set of conjugacy classes in G such that O intersects S and dim O=codim S. The construction of the slice utilizes some new combinatorics related to invariant planes for the action of Weyl group elements in the reflection representation. The condition dim O=codim S is checked using some new mysterious results by Lusztig on intersection of conjugacy classes in algebraic groups with Bruhat cells.