Whittaker functions on quantum groups and q-deformed Toda operators
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- January 1999
- DOI:
- 10.48550/arXiv.math/9901053
- arXiv:
- arXiv:math/9901053
- Bibcode:
- 1999math......1053E
- Keywords:
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- Quantum Algebra
- E-Print:
- 17 pages, amstex