Givental Integral Representation for Classical Groups

Details Givental Integral Representation for Classical Groups Givental Integral Representation for Classical Groups

2006-08-06

arxiv.org/abs/math/0608152v2

Mathematics

Representation Theory

Typos are corrected, Section 5 is extended, AmsLaTex, 19 pages

Scientific paper

We propose integral representations for wave functions of B_n, C_n, and D_n open Toda chains at zero eigenvalues of the Hamiltonian operators thus generalizing Givental representation for A_n. We also construct Baxter Q-operators for closed Toda chains corresponding to Lie algebras B_{\infty}, C_{\infty}, D_{\infty}, 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 A_n^{(1)} closed Toda chain and Givental representation for the wave function of A_n open Toda chain uncovered previously.

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