New Integral Representations of Whittaker Functions for Classical Lie Groups
arXiv:0705.2886
Abstract
We propose integral representations of the Whittaker functions for the classical Lie algebras sp(2l), so(2l) and so(2l+1). These integral representations generalize the integral representation of gl(l+1)-Whittaker functions first introduced by Givental. One of the salient features of the Givental representation is its recursive structure with respect to the rank of the Lie algebra gl(l+1). The proposed generalization of the Givental representation to the classical Lie algebras retains this property. It was shown elsewhere that the integral recursion operator for gl(l+1)-Whittaker function in the Givental representation coincides with a degeneration of the Baxter Q-operator for -Toda chains. We construct Q-operator for affine Lie algebras , and a twisted form of . We demonstrate that the relation between recursion integral operators of the generalized Givental representation and degenerate Q-operators remains valid for all classical Lie algebras.
100 pages