Multiple Hypergeometric Functions and Simple Lie Groups ${\bf {\text{SL}}}$ and ${\bf {\text{Sp}}}$

Abstract

With any multiple hypergeometric series one can associate a Lie group called its group of symmetries. This article is devoted to those series which group of symmetries contains a subgroup isomorphic to the special linear group ${\bf {\text{SL}}}$ or to the sympletic group ${\bf {\text{Sp}}}$. The work owes much to the group-theoretic analysis of the Lauricella series $F_D$ in Miller [J. Math. Phys.,13 (1972), pp. 1393–1399], Symmetry and the Separation of Variables, Addison-Wesley, Reading, MA, 1977.