Reducibility of Quantum Representations of Mapping Class Groups

被引:5
|
作者
Andersen, Jorgen Ellegaard [1 ]
Fjelstad, Jens [2 ]
机构
[1] Univ Aarhus, Ctr Quantum Geometry Moduli Spaces, DK-8000 Aarhus, Denmark
[2] Karlstad Univ, Dept Phys, S-65188 Karlstad, Sweden
基金
新加坡国家研究基金会;
关键词
topological quantum field theory; mapping class group; quantum representation; CONFORMAL FIELD-THEORY; INVARIANT PARTITION-FUNCTIONS; MODULAR INVARIANTS; TFT CONSTRUCTION; GEOMETRIC-QUANTIZATION; KAUFFMAN BRACKET; ALPHA-INDUCTION; SIMPLE CURRENTS; CLASSIFICATION; CATEGORIES;
D O I
10.1007/s11005-009-0367-7
中图分类号
O4 [物理学];
学科分类号
0702 ;
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.
引用
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页码:215 / 239
页数:25
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