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Symmetry, Integrability and Geometry: Methods and Applications, 2014, Volume 10, 026, 29 pp.
DOI: https://doi.org/10.3842/SIGMA.2014.026
(Mi sigma891)
 

This article is cited in 4 scientific papers (total in 4 papers)

Symmetry Groups of $A_n$ Hypergeometric Series

Yasushi Kajihara

Department of Mathematics, Kobe University, Rokko-dai, Kobe 657-8501, Japan
Full-text PDF (519 kB) Citations (4)
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Abstract: Structures of symmetries of transformations for Holman–Biedenharn–Louck $A_n$ hypergeometric series: $A_n$ terminating balanced ${}_4 F_3$ series and $A_n$ elliptic ${}_{10} E_9$ series are discussed. Namely the description of the invariance groups and the classification all of possible transformations for each types of $A_n$ hypergeometric series are given. Among them, a “periodic” affine Coxeter group which seems to be new in the literature arises as an invariance group for a class of $A_n$ ${}_4 F_3$ series.
Keywords: multivariate hypergeometric series; elliptic hypergeometric series; Coxeter groups.
Received: September 30, 2013; in final form March 4, 2014; Published online March 18, 2014
Bibliographic databases:
Document Type: Article
Language: English
Citation: Yasushi Kajihara, “Symmetry Groups of $A_n$ Hypergeometric Series”, SIGMA, 10 (2014), 026, 29 pp.
Citation in format AMSBIB
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  • This publication is cited in the following 4 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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