A Spin Decomposition of the Verlinde Formulas for Type A Modular Categories
A Spin Decomposition of the Verlinde Formulas for Type A Modular Categories
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A型模范畴Verlinde公式的自旋分解
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发表时间：
2003
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通讯作者：
C. Blanchet
中科院分区：
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作者：
C. Blanchet
模范畴是带有一些附加代数特征的编织范畴。这个概念的有趣之处在于它提供了一个3维的拓扑量子场论。与模块类别相关联的Verlinde公式是TQFT模块的维度。对于与SU(N)相关的模范畴，我们讨论了这些公式的约简和改进。我们的主要结果是Verlinde公式的分裂，对应于TQFT模块的砖分解，其和由自旋结构模偶整数索引。本文引入自旋模范畴的概念，并在此一般情况下给出分解定理的证明。
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 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 here the notion of a spin modular category, and give the proof of the decomposition theorem in this general context.