Monday, December 5th, 2005
2:30pm - 3:30pm, in Science 2-065

Steven Jackson

UMass Boston

Prehomogeneous Spaces Associated With Real Nilpotent Orbits

Abstract: Let g_0 be a real semisimple Lie algebra. Each conjugacy class of nilpotent elements in g_0 gives rise via the Kostant-Sekiguchi correspondence to a Z-grading on the associated symmetric pair (g,k), with respect to which each homogeneous component is a prehomogeneous vector space under the natural action of K_0. In this talk, we discuss methods for the determination of the isomorphism types and relative invariants of these prehomogeneous spaces from combinatorial data attached to the nilpotent orbit. This is joint work with Alfred Noël.