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arXiv · 0805.3754

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

Anton Gerasimov·Dimitri Lebedev·Sergey Oblezin
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Abstract

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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Anton Gerasimov, Dimitri Lebedev, Sergey Oblezin. 2008-06-11. On q-deformed gl(l+1)-Whittaker function III. https://arxiv.org/abs/0805.3754

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