ALT

Abstract

The definition of q,t-spherical functions was sugested by the speaker (reduced root systems) and Stokman (the C-check-C case). They generalize the classical spherical functions, the basic hypergeometric function and the p-adic spherical functions. Recently, their systematic algebraic and analytic theory was started including q-generalizations of the Harish-Chandra asymtotic formula and the Helgason-Johnson description of bounded spherical functions, as well as the theory of the q-Whittaker functions. The latter are related to the Givental-Lee theory, the IC-theory of the affine flag varieties and are expected to have connections with the quantum geometric Langlands program.