On q-deformed gl(l+1)-Whittaker function III
Anton Gerasimov, Dimitri Lebedev, and Sergey Oblezin
TL;DR
This paper connects q-deformed gl(l+1)-Whittaker functions to Macdonald polynomials, Demazure characters, and quantum algebra, providing new representations and integral formulas for these functions.
Contribution
It identifies q-deformed gl(l+1)-Whittaker functions with Macdonald polynomial specializations and introduces dual Hamiltonians and matrix element representations.
Findings
Representation in terms of Demazure characters
New integral representation for q-deformed Whittaker functions
Expression as a matrix element of quantum torus algebra
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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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Mathematical Identities · Mathematical functions and polynomials