This article is cited in 4 papers

Decomposition of some Witten–Reshetikhin–Turaev Representations into Irreducible Factors

Julien Korinman

Fundação Universidade Federal de São Carlos, Departamento de Matemática, Rod. Washington Luís, Km 235, C.P. 676, 13565-905 São Carlos, SP, Brasil

Abstract: We decompose into irreducible factors the ${\rm SU}(2)$ Witten–Reshetikhin–Turaev representations of the mapping class group of a genus $2$ surface when the level is $p=4r$ and $p=2r^2$ with $r$ an odd prime and when $p=2r_1r_2$ with $r_1$, $r_2$ two distinct odd primes. Some partial generalizations in higher genus are also presented.

Keywords: Witten–Reshetikhin–Turaev representations; mapping class group; topological quantum field theory.

MSC: 57R56; 57M60

Received: October 29, 2017; in final form January 30, 2019; Published online February 12, 2019

Language: English

DOI: 10.3842/SIGMA.2019.011

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ArXiv: 1406.4389