%0 Journal Article
%T Whittaker functions on quantum groups and q-deformed Toda operators
%A Pavel Etingof
%J Mathematics
%D 1999
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/9901053v1