Symmetry Groups of $A_n$ Hypergeometric Series

Yasushi Kajihara

Symmetry, integrability and geometry: methods and applications, Tome 10 (2014)

Résumé

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.

Détail

Keywords: multivariate hypergeometric series; elliptic hypergeometric series; Coxeter groups.

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