Givental Integral Representation for Classical Groups

2006/08/06 by A. Gerasimov, Gerasimov, A., D. V. Lebedev +5
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #advanced mathematical theories #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0608152

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

openalex publication_date 2006/08/06 · arxiv created 2006/08/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_∞, 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 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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