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This article is cited in 5 scientific papers (total in 5 papers)
Basic Properties of Non-Stationary Ruijsenaars Functions
Edwin Langmanna, Masatoshi Noumibc, Junichi Shiraishid a Physics Department, KTH Royal Institute of Technology, SE-106 91 Stockholm, Sweden
b Department of Mathematics, KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden
c Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
d Graduate School of Mathematical Sciences, The University of Tokyo, Komaba,
Tokyo 153-8914, Japan
Abstract:
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.
Keywords:
elliptic integrable systems, elliptic hypergeometric functions, Ruijsenaars systems.
Received: June 15, 2020; in final form October 8, 2020; Published online October 21, 2020
Citation:
Edwin Langmann, Masatoshi Noumi, Junichi Shiraishi, “Basic Properties of Non-Stationary Ruijsenaars Functions”, SIGMA, 16 (2020), 105, 26 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1642 https://www.mathnet.ru/eng/sigma/v16/p105
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