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Article overview
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New Integral Representations of Whittaker Functions for Classical Lie
Groups | A. Gerasimov
; D. Lebedev
; S. Oblezin
; | Date: |
20 May 2007 | Subject: | Representation Theory (math.RT) | 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 $hat{gl(l+1)}$-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. | Source: | arXiv, arxiv.0705.2886 | Services: | Forum | Review | PDF | Favorites |
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