Diagonalization of the elliptic Macdonald-Ruijsenaars difference system of typeC₂

DOI10.1088/0305-4470/34/26/308zbMATH Open1051.39021arXivmath/9912114OpenAlexW2592592433MaRDI QIDQ4816614

Publication date: 10 September 2004

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: We study a pair of commuting difference operators arising from the elliptic solution of the dynamical Yang-Baxter equation of type C_2. The operators act on the space of meromorphic functions on the weight space of sp(4,C). We show that these operators can be identified with the system by van Diejen and by Komori-Hikami with special parameters. It turns out that our case can be related to the difference Lame operator (two-body Ruijsenaars operator) and thereby we diagonalize the system on the finite dimensional space spanned by the level one characters of the C_2^{(1)}-affine Lie algebra.

Full work available at URL: https://arxiv.org/abs/math/9912114

zbMATH Keywords

Lie algebra difference operators diagonalization dynamical Yang-Baxter equation two-body Ruijsenaars operator difference Lamé operator elliptic Macdonald-Ruijsenaars difference system

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Groups and algebras in quantum theory and relations with integrable systems (81R12) Difference operators (39A70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Diagonalization of the elliptic Macdonald-Ruijsenaars difference system of typeC2

Diagonalization of the elliptic Macdonald-Ruijsenaars difference system of typeC₂