Felder's elliptic quantum group and elliptic hypergeometric series on the root system A_n

TL;DR

This paper introduces a generalization of elliptic 6j-symbols linked to Felder's elliptic quantum group, expressing them via multivariable elliptic hypergeometric series on the A_n root system, leading to new biorthogonality relations.

Contribution

It presents a novel generalization of elliptic 6j-symbols and connects them to multivariable elliptic hypergeometric series, expanding the understanding of elliptic quantum groups.

Findings

New elliptic 6j-symbols generalized for Felder's elliptic quantum group

Expression of these symbols in terms of multivariable elliptic hypergeometric series

Derivation of new biorthogonality relations for these series

Abstract

We introduce a generalization of elliptic 6j-symbols, which can be interpreted as matrix elements for intertwiners between corepresentations of Felder's elliptic quantum group. For special parameter values, they can be expressed in terms of multivariable elliptic hypergeometric series related to the root system A_n. As a consequence, we obtain new biorthogonality relations for such series.