An Alternative Description of the Quantum GroupSUq(2) and the q-Analog Racah-Wigner Algebra

Abstract

A set of generators of the quantum group S U q (2) is presented which yields the q -analog Racah-Wigner (RW) algebra. While the standard specification of S U q (2) requires separate treatment for different components of a tensor, the present approach gives unified treatment of tensor algebra. Clebsch-Gordan (CG) and Racah coefficients are extensively used. This unified treatment is crucial to formulate the q -analog irreducible tensor operator and Wigner-Eckart theorem. Witten's specification of S U q (2), exploited in rational conformal field theories (RCFT), is realized in the present approach.