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We propose integral representations of the Whittaker functions for the classical Lie algebras sp2l, so2l and so2l+1. These integral representations generalize the integral representation of gll+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 l of the Lie algebra gll+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 gll+1-Whittaker function in the Givental representation coincides with a degeneration of the Baxter Q-operator for ĝll+1-Toda chains. We construct Q-operator for affine Lie algebras ŝo2l, ŝo2l+1 and a twisted form of ĝl2l. 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. E-mail: lebedev@itep.ru E-mail: Sergey.Oblezin@itep.ru

Новые интегральные представления функций Уиттекера для классических групп Ли