Scattering theory of discrete (pseudo) Laplacians on a Weyl chamber

Abstract

To a crystallographic root system we associate a system of multivariate orthogonal polynomials diagonalizing an integrable system of discrete pseudo Laplacians on the Weyl chamber. We develop the time-dependent scattering theory for these discrete pseudo Laplacians and determine the corresponding wave operators and scattering operators in closed form. As an application, we describe the scattering behavior of certain hyperbolic Ruijsenaars-Schneider type lattice Calogero-Moser models associated with the Macdonald polynomials.

31 pages, LaTeX

Cited by in corpus (7)

• The semi-infinite q-boson system with boundary interaction
• Integrable boundary interactions for Ruijsenaars' difference Toda chain
• An (inverse) Pieri formula for Macdonald polynomials of type C
• Spectrum and eigenfunctions of the lattice hyperbolic Ruijsenaars-Schneider system with exponential Morse term
• Hypercomplex Fock States for Discrete Electromagnetic Schrödinger Operators: A Bayesian Probability Perspective
• Quantum Integrals for a Semi-Infinite $q$-Boson System with Boundary Interactions
• A Pieri formula for Macdonald's spherical functions and polynomials