Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 16 (2020), 088, 21 pages      arXiv:2005.02203      https://doi.org/10.3842/SIGMA.2020.088
Contribution to the Special Issue on Elliptic Integrable Systems, Special Functions and Quantum Field Theory

Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems

Hjalmar Rosengren a and Michael J. Schlosser b
a) Department of Mathematics, Chalmers University of Technology and the University of Gothenburg, SE-412 96 Göteborg, Sweden
b) Fakultät für Mathematik der Universität Wien, Oskar Morgenstern-Platz 1, A-1090 Wien, Austria

Received May 06, 2020, in final form August 28, 2020; Published online September 24, 2020

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 $A_r$ elliptic Jackson summation, as well as several quadratic, cubic and quartic summation formulas.

Key words: elliptic hypergeometric series; hypergeometric series associated with root systems; multidimensional matrix inversion.

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