2007-02-23
Ivan Losev, Moscow State University and Rutgers University
A uniqueness property for smooth affine spherical varieties
Let G be a connected reductive algebraic group over an
algebraically closed field of characteristic 0. A normal irreducible
G-variety X is called spherical if a Borel subgroup
of G has an open orbit on X. It was conjectured by
F. Knop that two smooth affine spherical G-varieties with the
same weight monoids are isomorphic as G-varieties. Here by
the weight monoid of X we mean the set of highest weights of
the algebra of regular functions on X considered as a
G-module. It was proved by Knop that this conjecture implies
a uniqueness property for multiplicity free Hamiltonian actions of
compact groups on compact real manifolds (the Delzant conjecture). In
the talk I am going to outline my recent proof of Knop's conjecture
(arXiv:math.AG/0612561).