Fusion Rules and R-Matrices For Representations of $SL(2{)}_q$ at Roots of Unity

Abstract

We recall the classification of the irreducible representations of $SL(2{)}_q$, and then give fusion rules for these representations. We also consider the problem of $\cR$-matrices, intertwiners of the differently ordered tensor products of these representations, and satisfying altogether Yang--Baxter equations.

13 pages. This is a contribution to the Vth Conference on Mathematical Physics, Edirne, Turkey 15-22 Dec. 1991

References in corpus (1)

• New Solutions to the Yang--Baxter Equation from Two--Dimensional Representations of $U_q(sl(2))$ at Roots of Unit

Cited by in corpus (5)

• Quantum deformation of two four-dimensional spin foam models
• Quasilocal conservation laws from semicyclic irreducible representations of $U_q({\mathfrak{sl}}_2)$ in $XXZ$ spin-$1/2$ chains
• Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
• R-matrices for highest weight representations of sl_q(2,C) at roots of unity
• R-matrices of U_qOSP(1,2) for highest weight representations of U_qOSP(1,2) for general q and q is an odd root of unity