A proof of a multivariable elliptic summation formula conjectured by Warnaar. (Q2782417)

Elliptic hypergeometric series were introduced by Frenkel and Turaev in their study of elliptic \(6j\)-symbols corresponding to certain elliptic solutions of the Yang-Baxter equation [see \textit{I. B. Frenkel} and \textit{V. G. Turaev}, in: Arnold, V.I. (ed.) et al., The Arnold-Gelfand mathematical seminars: geometry and singularity theory, 171--204 (1997; Zbl 0974.17016)]. In [Summation and transformation formulas for elliptic hypergeometric series (preprint math.QA/0001006)], \textit{S. O. Warnaar} investigated multivariable versions of the elliptic hypergeometric series. He also conjectured a certain generalization (connected with the root system \(C_n\)) of the elliptic Jackson-Dougall summation formula of Frenkel and Turaev. The proof of this conjecture is the central result of the paper under review. Its main tool is another generalization of the elliptic Jackson-Dougall summation formula proven by Warnaar [loc. cit.].NEWLINENEWLINEFor the entire collection see [Zbl 0980.00024].