2007/05/20 by A. Gerasimov, Gerasimov, A., D. V. Lebedev +5 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.0705.2886
100 pages
arxiv created 2007/05/20 · openalex publication_date 2007/05/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 gl(l+1)-Toda chains. We construct Q-operator for affine Lie algebras so(2l), so(2l+1) and a twisted form of gl(2l). 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.