Structures of symmetries of transformations for Holman-Biedenharn-Louck An
hypergeometric series: An terminating balanced 4F3 series and An
elliptic 10E9 series are discussed. Namely the description of the
invariance groups and the classification all of possible transformations for
each types of An 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 An4F3 series