Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems

Symmetry Integrability and Geometry-Methods and Applications

article

Hjalmar Rosengren¹  Michael J. Schlosser² 

[1] Department of Mathematics, Chalmers University of Technology and the University of Gothenburg;Fakultät für Mathematik der Universität Wien

关键词: elliptic hypergeometric series;    hypergeometric series associated with root systems;    multidimensional matrix inversion 2020 Mathematics Subject Classification 33D67;   

DOI  :  10.3842/SIGMA.2020.088

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown