On Hypergeometric Series Well-Poised in $SU(n)$

Abstract

By exploiting the known relationship between well-poised hypergeometric series and the combinatorial aspects of the representation theory of $SU(2)$, we define a generalization of the well-poised concept for multidimensional series adapted to $SU(n)$ symmetry. The analogue to Whipple’s theorem is demonstrated for $SU(3)$, and the analogue to the well-poised ${}_4 F_3 ( - 1)$ theorem is given for all $SU(n)$.