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Symmetry, Integrability and Geometry: Methods and Applications, 2020, Volume 16, 105, 26 pp.
DOI: https://doi.org/10.3842/SIGMA.2020.105
(Mi sigma1642)
 

This article is cited in 6 scientific papers (total in 6 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
Full-text PDF (525 kB) Citations (6)
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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.
Funding agency Grant number
VR grant 2016-05167
Japan Society for the Promotion of Science (B) 15H03626
(C) 19K03512
Knut and Alice Wallenbergs Foundation KAW 2019.0525
Stiftelsen Olle Engkvist Byggmästare 184-0573
This work is supported by VR Grant No 2016-05167 (E.L.) and by JSPS Kakenhi Grants (B) 15H03626 (M.N.), (C) 19K03512 (J.S.). MN gratefully acknowledges financial support by the Knut and Alice Wallenberg foundation (KAW 2019.0525). We are grateful to the Stiftelse Olle Engkvist Byggmästare, Contract 184-0573, for financial support.
Received: June 15, 2020; in final form October 8, 2020; Published online October 21, 2020
Bibliographic databases:
Document Type: Article
Language: English
Citation: Edwin Langmann, Masatoshi Noumi, Junichi Shiraishi, “Basic Properties of Non-Stationary Ruijsenaars Functions”, SIGMA, 16 (2020), 105, 26 pp.
Citation in format AMSBIB
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\by Edwin~Langmann, Masatoshi~Noumi, Junichi~Shiraishi
\paper Basic Properties of~Non-Stationary Ruijsenaars Functions
\jour SIGMA
\yr 2020
\vol 16
\papernumber 105
\totalpages 26
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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