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MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics



Funded by The Danish National Research Foundation
Geometric Mathematical Physics Seminar
Wednesday, 3 November 2004, at 16:15 in D3
Christian Blanchet
Université de Bretagne-Sud, France
A spin decomposition of the Verlinde formulas for type A modular categories

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.