On q-deformed gl(l+1)-Whittaker function II

Abstract

A representation of a specialization of a q-deformed class one lattice gl(\ell+1}-Whittaker function in terms of cohomology groups of line bundles on the space QM_d(P^{\ell}) of quasi-maps P^1 to P^{\ell} of degree d is proposed. For \ell=1, this provides an interpretation of non-specialized q-deformed gl(2)-Whittaker function in terms of QM_d(\IP^1). In particular the (q-version of) Mellin-Barnes representation of 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 substitute of topological genus in semi-infinite geometry. A relation with Givental-Lee universal solution (J-function) of q-deformed gl(2)-Toda chain is also discussed.

Extended version submitted in Comm. Math. Phys., 24 pages

References in corpus (5)

• Finite difference quantum Toda lattice via equivariant K-theory
• Baxter operator and Archimedean Hecke algebra
• Representation Theory and the Quantum Inverse Scattering Method: The Open Toda Chain and the Hyperbolic Sutherland Model
• On Baxter Q-operators And Their Arithmetic Implications
• New Integral Representations of Whittaker Functions for Classical Lie Groups

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