  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.
