On q-Deformed gll+1-Whittaker Function II

A representation of a specialization of a q-deformed class one lattice gl(l+1)-Whittaker function in terms of cohomology groups of line bundles on the space QM(d) (P-l) of quasi-maps P-1 -> P-l of degree d is proposed. For l = 1, this provides an interpretation of the non-specialized q-deformed gl(2)-Whittaker function in terms of QM(d) (P-1). In particular the (q-version of the) Mellin-Barnes representation of the gl(2)-Whittaker function is realized as a semi-infinite period map. The explicit form of the period map manifests an important role of q-version of Gamma-function as a topological genus in semi-infinite geometry. A relation with the Givental-Lee universal solution (J-function) of q-deformed gl(2)-Toda chain is also discussed.