# Seminario: A Katsylo theorem for sheets of spherical conjugacy classes

## Lunedì 30 Marzo 2015, ore 14:00 - Aula 1BC45 - Giovanna Carnovale

ARGOMENTI: Seminari

Seminario

Lunedì 30 Marzo 2015 alle ore 14:00 in aula 1BC45, Giovanna Carnovale terrà un seminario dal titolo "A Katsylo theorem for sheets of spherical conjugacy classes".

Abstract
A sheet for the action of a linear algebraic group is an irreducible component of the set of points whose orbit has fixed dimension. Katsylo proved in 1982 that the geometric quotient $S/G$, for $S$ a sheet in the Lie algebra of a reductive group $G$ over ${\mathbb C}$, is isomorphic to $(S\cap {\mathcal S}_e)/A(e)$, where $e$ is a nilpotent element in $S$, ${\mathcal S}_e$ is the corresponding Slodowy slice and $A(e)$ is its component group. We will present an analogue of this statement for sheets of spherical conjugacy classes in $G$. A version of this result where sheets are replaced by the parts in a partition recently introduced by G. Lusztig also holds. As a biproduct one obtains that all sheets of spherical conjugacy classes are smooth.