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

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

1991-12-10

arxiv.org/abs/hep-th/9112022v2

Phys.Lett. B280 (1992) 31-38

Physics

High Energy Physics

High Energy Physics - Theory

12 pages

Scientific paper

10.1016/0370-2693(92)90768-Y

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.

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