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

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

2008-05-24

arxiv.org/abs/0805.3754v2

Mathematics

Representation Theory

20 pages, several typos corrected

Scientific paper

We identify q-deformed gl(l+1)-Whittaker functions with a specialization of Macdonald polynomials. This provides a representation of q-deformed gl(l+1)-Whittaker functions in terms of Demazure characters of affine Lie algebra \hat{gl(l+1)}. We also define a system of dual Hamiltonians for q-deformed gl(l+1)-Toda chains and give a new integral representation for q-deformed gl(l+1)-Whittaker functions. Finally an expression of q-deformed gl(l+1)-Whittaker function as a matrix element of a quantum torus algebra is derived.

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