Multidimensional matrix inversions and elliptic hypergeometric series on root systems

Hjalmar Rosengren, Michael J. Schlosser

Published 2020-05-05Version 1

Multidimensional matrix inversions is 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 $A_r$ elliptic Jackson summation, as well as several quadratic, cubic and quartic summation formulas.