# The wonderful compactication and the universal centralizer

Let $G$be a complex semisimple algebraic group of adjoint type and $\overline{G}$ the wonderful compacti

cation. We show that the closure in \overline{G} of the centralizer $G^e$of a regular nilpotent $e \in Lie(G)$is isomorphic to the Peterson variety. We generalize this result to show that for any regular $x \in Lie(G)$, the closure of the centralizer $G^x$in $\overline{G}$is isomorphic to the closure of a general $G^x$-orbit in the flag variety. We consider the family of all such centralizer closures, which is a partial compactication of the universal centralizer. We show that it has a natural log-symplectic Poisson structure that extends the usual symplectic structure on the universal centralizer.

Collection/Series:
Event Type:
Seminar
Scientific Area(s):
Speaker(s):
Event Date:
Lundi, Février 26, 2018 - 14:00 to 15:30
Location:
Sky Room
Room #:
394