Elliptic Ruijsenaars difference operators on bounded partitions

Abstract

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 corresponding orthogonal basis of joint eigenfunctions is constructed in terms of polynomials on the joint spectrum. In the trigonometric limit, this recovers the diagonalization of the truncated Macdonald difference operators by a finite-dimensional basis of Macdonald polynomials.

14 pages, v2: minor corrections and reference added

References in corpus (3)

• Duality in elliptic Ruijsenaars system and elliptic symmetric functions
• Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism
• Construction of eigenfunctions for the elliptic Ruijsenaars difference operators

Cited by in corpus (4)

• Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and R-matrix identities
• Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n{)}^{\ast }$-valued spins from Poisson reduction
• Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry
• Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess-Zumino-Witten fusion rings