Givental Integral Representation for Classical Groups
Representation Theory
2007-05-23 v2 Quantum Algebra
Abstract
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.
Cite
@article{arxiv.math/0608152,
title = {Givental Integral Representation for Classical Groups},
author = {A. Gerasimov and D. Lebedev and S. Oblezin},
journal= {arXiv preprint arXiv:math/0608152},
year = {2007}
}
Comments
Typos are corrected, Section 5 is extended, AmsLaTex, 19 pages