On q-deformation of gl(N)-Whittaker function

Abstract:

In my talk I'll present my recent results (joint with A.Gerasimov and D.Lebedev) on q-deformations of Whittaker functions. We construct two (dual) representations of q-Whittaker functions, and consider a set of interpretations and applications of these formulas. A special attention in my talk will be given to relations with Archimedean version of Casselman-Shalika formula, with Demazure characters, and with quantum cohomology of flag spaces and Gamma-genus

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