Symmetry Groups of $A_n$ Hypergeometric Series

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.

References in corpus (4)

• Properties of generalized univariate hypergeometric functions
• Coxeter group actions on Saalschützian ${}_4{F}_3(1)$ series and very-well-poised ${}_7{F}_6(1)$ series
• Coxeter group actions on 4F3(1) hypergeometric series
• Multiple basic hypergeometric transformation formulas arising from the balanced duality transformation

Cited by in corpus (2)

• Terminating basic hypergeometric representations and transformations for the Askey-Wilson polynomials
• Transformation formulas for bilinear sums of basic hypergeometric series