Basic Properties of Non-Stationary Ruijsenaars Functions

Symmetry Integrability and Geometry-Methods and Applications

article

Edwin Langmann¹  Masatoshi Noumi²  Junichi Shiraishi³ 

[1] Physics Department, KTH Royal Institute of Technology;Department of Mathematics, KTH Royal Institute of Technology;Graduate School of Mathematical Sciences, The University of Tokyo

关键词: elliptic integrable systems;    elliptic hypergeometric functions;    Ruijsenaars systems 2020 Mathematics Subject Classification 81Q80;    32A17;    33E20;    33E30;   

DOI  :  10.3842/SIGMA.2020.105

来源: National Academy of Science of Ukraine

【 摘 要 】

For any variable number, a non-stationary Ruijsenaars function was recently introduced as a natural generalization of an explicitly known asymptotically free solution of the trigonometric Ruijsenaars model, and it was conjectured that this non-stationary Ruijsenaars function provides an explicit solution of the elliptic Ruijsenaars model. We present alternative series representations of the non-stationary Ruijsenaars functions, and we prove that these series converge. We also introduce novel difference operators called ${\mathcal T}$ which, as we prove in the trigonometric limit and conjecture in the general case, act diagonally on the non-stationary Ruijsenaars functions.

【 授权许可】

Unknown