"Fusion" of the representations of quantum groups in the root of unity
Let us take some quantum group .It is known that it is possible to find
vertex operator algebra such that the
category or representations is equivalent to the category of representations
of the quantum group.Actually the
tensor structure in the category of representations of quantum group is also
has the VOA counterpart.But the
VOA corresponding to the quantum group is not unique -there are a lot of
them.Such VOA defines some
additional structures on the category of representations of quantum group .
The "fusion" product is one
of such structures.I will try to explain what is happening in the simplest
sl(2) case.