The Arkhipov-Bezrukavnikov Equivalence and Categorifications of the Anti-Spherical Module

Watch a mathematics seminar presentation exploring the three distinct descriptions of the anti-spherical module for the affine Hecke algebra and their categorifications. Delve into Colton Sandvik's detailed explanation of the Arkhipov-Bezrukavnikov equivalence, which unifies these different categorifications. Learn about crucial sheaf classes in automorphic theory, including central sheaves, Wakimoto sheaves, and Iwahori-Whittaker sheaves, while understanding how the anti-spherical module can be interpreted as a quotient of regular representation, equivariant K-theory of Springer resolution, and Whittaker functions space on the affine flag variety.