A new dynamical reflection algebra and related quantum integrable systems

Abstract

We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang-Baxter equations, coactions, fusions, and commuting traces are derived. Explicit examples are given and quantum integrable Hamiltonians are constructed. They exhibit features similar to the Ruijsenaars-Schneider Hamiltonians.

16 pages v2: signs in the classical reflection algebra corrected

References in corpus (3)

• Parametrization of semi-dynamical quantum reflection algebra
• On the semi-dynamical reflection equation: solutions and structure matrices
• Quantum Dynamical coBoundary Equation for finite dimensional simple Lie algebras

Cited by in corpus (5)

• Rational Calogero-Moser Model: Explicit Form and r-Matrix of the Second Poisson Structure
• Connection problems for quantum affine KZ equations and integrable lattice models
• Classical r-matrix structure for elliptic Ruijsenaars chain and 1+1 field analogue of Ruijsenaars-Schneider model
• Algebraic structure of classical integrability for complex sine-Gordon
• Connection coefficients for basic Harish-Chandra series