Ivan Losev

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 are equivariantly isomorphic provided their algebras of regular functions are isomorphic as G-modules. Knop proved 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).