Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems

Abstract

Multidimensional matrix inversions provide a powerful tool for studying multiple hypergeometric series. In order to extend this technique to elliptic hypergeometric series, we present three new multidimensional matrix inversions. As applications, we obtain a new 𝘈ᵣ elliptic Jackson summation, as well as several quadratic, cubic, and quartic summation formulas.