Multiplicity-free Uq(slN) 6-j symbols: Relations, asymptotics, symmetries

Abstract

A closed form expression for multiplicity-free quantum 6-j symbols (MFS) was proposed in [1] for symmetric representations of Uq(slN), which are the simplest class of multiplicity-free representations. In this paper we rewrite this expression in terms of q-hypergeometric series Φ34. We claim that it is possible to express any MFS through the 6-j symbol for Uq(sl2) with a certain factor. It gives us a universal tool for the extension of various properties of the quantum 6-j symbols for Uq(sl2) to the MFS. We demonstrate this idea by deriving the asymptotics of the MFS in terms of associated tetrahedron for classical algebra U(slN).Next we study MFS symmetries using known hypergeometric identities such as argument permutations and Sears' transformation. We describe symmetry groups of MFS. As a result we get new symmetries, which are a generalization of the tetrahedral symmetries and the Regge symmetries for N=2.