Givental Integral Representation for Classical Groups
Abstract
We propose integral representations for wave functions of Bn, Cn, and Dn open Toda chains at zero eigenvalues of the Hamiltonian operators thus generalizing Givental representation for An. We also construct Baxter Q-operators for closed Toda chains corresponding to Lie algebras B∞, C∞, D∞, affine Lie algebras B(1)n, C(1)n, D(1)n and twisted affine Lie algebras A(2)2n-1 and A(2)2n. Our approach is based on a generalization of the connection between Baxter Q-operator for An(1) closed Toda chain and Givental representation for the wave function of An open Toda chain uncovered previously.
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