A Spin Decomposition of the Verlinde Formulas for Type a Modular Categories
نویسنده
چکیده
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 dimensions of the TQFT modules. We compute this formulas and discuss reductions and refinements 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 here the notion of a spin modular category, and give the proof of the decomposition theorem in this general context.
منابع مشابه
Vertex operator algebras, the Verlinde conjecture, and modular tensor categories.
Let V be a simple vertex operator algebra satisfying the following conditions: (i) V(n)) = 0 for n < 0, V(0)=C1, and the contragredient module V' is isomorphic to V as a V-module; (ii) every N-gradable weak V-module is completely reducible; (iii) V is C(2)-cofinite. We announce a proof of the Verlinde conjecture for V, that is, of the statement that the matrices formed by the fusion rules among...
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تاریخ انتشار 2001