Hanspeter Kraft

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.