3j-symbol for the modular double of SL_q(2,R) revisited

TL;DR

This paper revisits the decomposition of tensor products in the modular double of SL_q(2,R), providing detailed derivations and new proofs for the structure of these representations.

Contribution

It offers a more detailed derivation and new proofs for the tensor product decomposition in the modular double of SL_q(2,R).

Findings

Enhanced understanding of the tensor product decomposition

New proofs for the structure of irreducible representations

Clarification of the representation parameterization

Abstract

Modular double of quantum group SL_q(2,R) with |q|=1 has a series of selfadjoint irreducible representations parameterized by s. Ponsot and Teschner considered a decomposition of the tensor product of two representations into irreducibles. In our paper we give more detailed derivation and some new proofs.