Monday, February 26th, 2007
2:30pm - 3:30pm, in Science 2-065

Elizabeth Mann

MIT

Langlands duality for real groups, via the affine Grassmannian

Abstract: The Langlands dual of a complex group arises naturally out of the geometry of its affine Grassmannian. I'll begin by briefly reviewing this classical (geometric) Satake isomorphism, as well as its extension by Kazhdan and Lusztig to the affine Hecke algebra. I'll then describe the analogous statements & geometric picture for real groups. While a real group does not have a Langlands dual, a marvelous result of Vogan describes a duality on the irreducible admissible representations of real groups; and it is this duality which arises in our geometric picture.