Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A spin decomposition of the Verlinde formula for type A modular
  categories   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 the notion of a
spin modular category, and give the proof of the decomposition theorem in this
general context.

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The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org