Congruence property and Galois symmetry of modular categories

Details Congruence property and Galois symmetry of modular categories Congruence property and Galois symmetry of modular categories

2012-01-31

arxiv.org/abs/1201.6644v2

Mathematics

Quantum Algebra

28 pages latex, some typos corrected. A reference, a remark (5.3) and a variation (5.5) of Proposition 3 in [CG2] are added, a

Scientific paper

In this paper, we prove the congruence property and Galois symmetry of the modular representations associated with any modular tensor category. The result was conjectured by Coste, Gannon, Eholzer and many other authors. We apply this result to determine the order of the anomaly $\alpha$ for those modular categories $A$ satisfying some integrality conditions. Moreover, if the global dimension $\dim A$ is an odd integer, we prove that the parity of the order of $\alpha$ is given by the Jacobi symbol $(\frac{-1}{\dim A})$.

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