Corpus ID: 236772182

Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry

  title={Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry},
  author={Jan Felipe van Diejen and Tam'as Gorbe},
We construct the orthogonal eigenbasis for a discrete elliptic Ruijsenaars type quantum particle Hamiltonian with hyperoctahedral symmetry. In the trigonometric limit the eigenfunctions in question recover a previously studied q-Racah type reduction of the Koornwinder-Macdonald polynomials. When the inter-particle interaction degenerates to that of impenetrable bosons, the orthogonal eigenbasis simplifies in terms of generalized Schur polynomials on the spectrum associated with recently found… Expand


Quantum integrability of the generalized elliptic Ruijsenaars models
The quantum integrability of the generalized elliptic Ruijsenaars models is shown. These models are mathematically related to the Macdonald operator and the Macdonald - Koornwinder operator, whichExpand
Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type I. The Eigenfunction Identities
In this series of papers we study Hilbert-Schmidt integral operators acting on the Hilbert spaces associated with elliptic Calogero-Moser type Hamiltonians. As shown in this first part, the integralExpand
Integrability of difference Calogero-Moser systems
A general class of n‐particle difference Calogero–Moser systems with elliptic potentials is introduced. Besides the step size and two periods, the Hamiltonian depends on nine coupling constants. WeExpand
Conserved operators of the generalized elliptic Ruijsenaars models
We construct the integrable families of the generalized elliptic Ruijsenaars models by use of the Yang–Baxter equation and the reflection equation. The higher order conserved operators of theseExpand
Elliptic Ruijsenaars difference operators on bounded partitions
By means of a truncation condition on the parameters, the elliptic Ruijsenaars difference operators are restricted onto a finite lattice of points encoded by bounded partitions. A correspondingExpand
Source Identities and Kernel Functions for the Deformed Koornwinder–van Diejen Models
We consider generalizations of the BC -type relativistic Calogero–Moser–Sutherland models, comprising of the rational, trigonometric, hyperbolic, and elliptic cases, due to Koornwinder and vanExpand
Difference Calogero-Moser systems and finite Toda chains
Limits of a recently introduced n‐particle difference Calogero–Moser system with elliptic potentials are studied. We obtain hyperbolic and rational difference Calogero–Moser systems with anExpand
Multivariable q-Racah polynomials
The Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials is studied for parameters satisfying a truncation condition such that the orthogonality measure becomes discreteExpand
Askey-Wilson polynomials for root systems of type BC
This paper introduces a family of Askey-Wilson type orthogonal polynomials in n variables associated with a root system of type BCn. The family depends, apart from q, on 5 parameters. For n = 1 itExpand
Elliptic Functions and Applications
1 Theta Functions.- 2 Jacobi's Elliptic Functions.- 3 Elliptic Integrals.- 4 Geometrical Applications.- 5 Physical Applications.- 6 Weierstrass's Elliptic Function.- 7 Applications of the WeierstrassExpand