Multiplicity-free U q ( sl N ) 6-j symbols: Relations, asymptotics, symmetries

摘要

A closed form expression for multiplicity-free quantum 6-j symbols (MFS) was proposed in for symmetric representations ofUq(slN), which are the simplest class of multiplicity-free representations. In this paper we rewrite this expression in terms of q-hypergeometric seriesΦ34. We claim that it is possible to express any MFS through the 6-j symbol forUq(sl2)with a certain factor. It gives us a universal tool for the extension of various properties of the quantum 6-j symbols forUq(sl2)to the MFS. We demonstrate this idea by deriving the asymptotics of the MFS in terms of associated tetrahedron for classical algebraU(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 forN=2.