On Lusztig's map for spherical unipotent conjugacy classes

Abstract

We provide an alternative description of the restriction to spherical unipotent conjugacy classes, of Lusztig's map Psi from the set of unipotent conjugacy classes in a connected reductive algebraic group to the set of conjugacy classes of its Weyl group. For irreducible root systems, we analyze the image of this restricted map and we prove that a conjugacy class in a finite Weyl group has a unique maximal length element if and only if it has a maximum.

Refereed version, one reference added. The final version will appear in the Bulletin of the London Mathematical Society

Cited by in corpus (1)

• A classification of spherical conjugacy classes