New fusion rules and $\cR$-matrices for $SL(N{)}_q$ at roots of unity

Abstract

We derive fusion rules for the composition of $q$-deformed classical representations (arising in tensor products of the fundamental representation) with semi-periodic representations of $SL(N{)}_q$ at roots of unity. We obtain full reducibility into semi-periodic representations. On the other hand, heterogeneous $\cR$-matrices which intertwine tensor products of periodic or semi-periodic representations with $q$-deformed classical representations are given. These $\cR$-matrices satisfy all the possible Yang Baxter equations with one another and, when they exist, with the $\cR$-matrices intertwining homogeneous tensor products of periodic or semi-periodic representations. This compatibility between these two kinds of representations has never been used in physical models.

12 pages

References in corpus (1)

• A Two Parameter Deformation of the SU(1/1) Superalgebra and the XY Quantum Chain in a Magnetic Field

Cited by in corpus (3)

• R-matrices for highest weight representations of sl_q(2,C) at roots of unity
• Quantum spin coverings and statistics
• 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