Reducibility of Quantum Representations of Mapping Class Groups

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作者
Jørgen Ellegaard Andersen
Jens Fjelstad
机构
[1] University of Aarhus,Center for Quantum Geometry of Moduli Spaces
[2] Karlstad University,Department of Physics
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57R56; topological quantum field theory; mapping class group; quantum representation;
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摘要
In this paper we provide a general condition for the reducibility of the Reshetikhin–Turaev quantum representations of the mapping class groups. Namely, for any modular tensor category with a special symmetric Frobenius algebra with a non-trivial genus one partition function, we prove that the quantum representations of all the mapping class groups built from the modular tensor category are reducible. In particular, for SU(N) we get reducibility for certain levels and ranks. For the quantum SU(2) Reshetikhin–Turaev theory we construct a decomposition for all even levels. We conjecture this decomposition is a complete decomposition into irreducible representations for high enough levels.
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页码:215 / 239
页数:24
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