New Integral Representations of Whittaker Functions for Classical Lie Groups

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dc.creatorGerasimov, A.
dc.creatorLebedev, D.
dc.creatorOblezin, S.
dc.date2007-05-20
dc.date.accessioned2026-07-07T08:02:34Z
dc.date.available2026-07-07T08:02:34Z
dc.descriptionWe 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 $\hat{gl(l+1)}$-Toda chains. We construct Q-operator for affine Lie algebras $\hat{so(2l)}$, $\hat{so(2l+1)}$ and a twisted form of $\hat{gl(2l)}$. 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.
dc.description100 pages
dc.identifierhttps://arxiv.org/abs/0705.2886
dc.identifierhttp://arxiv.org/abs/0705.2886
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129268
dc.subjectRepresentation Theory
dc.titleNew Integral Representations of Whittaker Functions for Classical Lie Groups
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