Abstract
A modular category is a braided category with some additional
algebraic features.
The interest of this concept is that it provides
a Topological Quantum Field Theory in dimension 3.
The Verlinde formulas associated with a modular category are the
dimension of the TQFT modules.
We discuss reductions and refinements of these formulas for
modular categories related with SU(N).
Our main result is a splitting of the Verlinde formula,
corresponding to a brick decomposition of the TQFT modules
whose summands are indexed by spin structures modulo
an even integer.
We introduce the notion of a spin modular category, and state the
decomposition theorem in this general context.
Contact person:Jørgen Ellegaard Andersen.