Programm des Emmy-Noether-Seminars

Fri, 28.10.2016, 14:30

End:
Fri, 28.10.2016, 15:30
Combinatorial characterization of the weight monoids of smooth affine spherical varieties
Emmy-Noether-Seminar

Speaker: Bart Van Steirteghem (FAU & CUNY)
Host: Knop
Room: 04.363

Let G be a connected complex reductive group. I. Losev has shown that a smooth affine spherical G-variety X is uniquely determined by its weight monoid, which is the set of irreducible representations of G that occur in the coordinate ring of X. This theorem had been conjectured by F. Knop, who also used it to show that multiplicity free (real) Hamiltonian manifolds are classified by their moment polytope and generic isotropy group.

I will present a combinatorial characterization of the weight monoids of smooth affine spherical varieties, obtained in joint work with G. Pezzini. It is a consequence of the combinatorial theory of spherical varieties and a smoothness criterion due to R. Camus. I will also discuss some applications developed with Pezzini and K. Paulus.