2008-10-31
Peter Trapa, University of Utah
Parametrizing Nilpotent Orbits in Semisimple Lie Algebras
About sixty years ago, Dynkin and Kostant classified adjoint
orbits of nilpotent elements in complex semisimple Lie algebras. This lead
to a complete parametrization of such orbits, but the parametrization often
involved case-by-case considerations. The purpose of this talk is to give a
uniform parametrization of certain orbits, namely those that arise in the
special piece of the closure of an even nilpotent orbit. The talk will focus
mainly on statements and examples, all of which are entirely elementary.
(But perhaps surprisingly the proofs are tied up with the theory of special
unipotent representations of the Langlands dual group in a rather intricate
way.) This is joint work with Dan Barbasch.