On the separation property of orbits


Hanspeter Kraft

( University of Basel )

Brandeis University

Thursday, February 15, 2001


Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall


Abstract:   A subvariety X of a complex vector space V is said to have the "separation property" if the following holds:

(SP) For any pair (a,b) of linearly independent linear functions on V there is a point x of X such that a(x) = 0 and b(x) not= 0.

We study this property in the case where V is a representation of a reductive group and X an orbit. So far, we have some partial results which, in particular, answer the original question asked by Jantzen:

"Does the highest weight orbit in the adjoint representation of a simple group have the separation property?"

It also turned out that there are interesting relations to problems concerning decompositions of tensor products.

Home Web page:  Alexandru I. Suciu  Created: February 12, 2001  Updated: February 13, 2001
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