Whittaker functions on quantum groups and q-deformed Toda operators
Quantum Algebra
2007-05-23 v1
Abstract
In this paper we q-deform a construction of Kazhdan and Kostant from 1970's which produces quantum Toda Hamiltonians by considering the action of Casimirs of a simple Lie algebra on Whittaker functions on the corresponding Lie group. We also give the affine analog of this generalization. This is done by extending the notion of a Whittaker function to quantum groups and quantum affine algebras. We compute the q-deformed Toda Hamiltonians for Lie algebras of type A and show that they coincide with those known in the theory of integrable systems.
Keywords
Cite
@article{arxiv.math/9901053,
title = {Whittaker functions on quantum groups and q-deformed Toda operators},
author = {Pavel Etingof},
journal= {arXiv preprint arXiv:math/9901053},
year = {2007}
}
Comments
17 pages, amstex