On a Classical Limit of q-Deformed Whittaker Functions

Previously, we derive a representation of q-deformed g(l+1)-Whittaker function as a sum over Gelfand-Zetlin patterns. This representation provides an analog of the Shintani-Casselman-Shalika formula for q-deformed gl(l+1)-Whittaker functions. In this note, we provide a derivation of the Givental integral representation of the classical gl(l+1)-Whittaker function as a limit q -> 1 of the sum over the Gelfand-Zetlin patterns representation of the q-deformed gl(l+1)-Whittaker function. Thus, Givental representation provides an analog the Shintani-Casselman-Shalika formula for classical Whittaker functions.