What is a 6-j symbol?

In representation theory, 6- j symbols are matrix coefficients of the associator isomorphism in a tensor category. For example, if we are given three representations Vi, Vj, Vk of a group (or quantum group ), one has a natural isomorphism

What is the asymptotic behavior of the 6-j symbol?

A remarkable formula for the asymptotic behavior of the 6- j symbol was first conjectured by Ponzano and Regge and later proven by Roberts. The asymptotic formula applies when all six quantum numbers j1., j6 are taken to be large and associates to the 6- j symbol the geometry of a tetrahedron.

When do the 6-j symbols become ordinary matrix coefficients?

where the sum is over all isomorphism classes of irreducible objects. Then: When the multiplicity spaces have canonical basis elements and dimension at most one (as in the case of SU (2) in the traditional setting), these component maps can be interpreted as numbers, and the 6- j symbols become ordinary matrix coefficients.