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Reducibility of quantum representations of mapping class groups
Center for Quantum Geometry of Moduli Spaces, University of Aarhus, Århus, Denmark.
Department of Physics, Karlstad University, Karlstad, Sweden.ORCID iD: 0000-0003-0372-5093
2010 (English)In: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 91, no 3, 215-239 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Springer, 2010. Vol. 91, no 3, 215-239 p.
Keyword [en]
topological quantum field theory; mapping class group; quantum representation
National Category
Other Mathematics Physical Sciences
Identifiers
URN: urn:nbn:se:oru:diva-57703DOI: 10.1007/s11005-009-0367-7ISI: 000275122700002Scopus ID: 2-s2.0-77949774852OAI: oai:DiVA.org:oru-57703DiVA: diva2:1096426
Note

Funding Agency:

Danish National Research Foundation Center of Excellence

Available from: 2014-11-25 Created: 2017-05-17 Last updated: 2017-05-18Bibliographically approved

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