Quantization and explicit diagonalization of new compactified trigonometric Ruijsenaars-Schneider systems

Abstract

Recently, Fehér and Kluck discovered, at the level of classical mechanics, new compactified trigonometric Ruijsenaars-Schneider $n$-particle systems, with phase space symplectomorphic to the $(n-1)$-dimensional complex projective space. In this article, we quantize the so-called type (i) instances of these systems and explicitly solve the joint eigenvalue problem for the corresponding quantum Hamiltonians by generalising previous results of van Diejen and Vinet. Specifically, the quantum Hamiltonians are realized as discrete difference operators acting in a finite-dimensional Hilbert space of complex-valued functions supported on a uniform lattice over the classical configuration space, and their joint eigenfunctions are constructed in terms of discretized $A_{n-1}$ Macdonald polynomials with unitary parameters.

arXiv comment27 pages, 4 figures

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Cited by in corpus (3)

• Elliptic Ruijsenaars difference operators on bounded partitions
• Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry
• Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess-Zumino-Witten fusion rings