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On relation of the genus one Moore-Seiberg identity to the Baxter Q-operator in the hyperbolic Ruijsenaars model

Elena Apresyan, Gor Sarkissian

Abstract

In this paper we show how the Baxter Q-operator and the product formula for eigenfunctions of two-particle hyperbolic Ruijsenaars system can be derived from the genus one Moore-Seiberg duality identity in two-dimensional Liouville conformal field theory. We expect that this relation would reveal genuine role of the Moore-Seiberg identity in integrable systems.

On relation of the genus one Moore-Seiberg identity to the Baxter Q-operator in the hyperbolic Ruijsenaars model

Abstract

In this paper we show how the Baxter Q-operator and the product formula for eigenfunctions of two-particle hyperbolic Ruijsenaars system can be derived from the genus one Moore-Seiberg duality identity in two-dimensional Liouville conformal field theory. We expect that this relation would reveal genuine role of the Moore-Seiberg identity in integrable systems.
Paper Structure (5 sections, 66 equations)

This paper contains 5 sections, 66 equations.

Table of Contents

  1. Introduction
  2. Evaluation of the RHS of the MS identity
  3. Evaluation of the LHS of the MS identity
  4. Conclusion
  5. Integral identities for hyperbolic gamma function