#### Vol. 294, No. 1, 2018

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Irreducible decomposition for local representations of quantum Teichmüller space

### Jérémy Toulisse

Vol. 294 (2018), No. 1, 233–256
##### Abstract

We give an irreducible decomposition of the so-called local representations (Bai, Bonahon and Liu, 2007) of the quantum Teichmüller space ${\mathsc{T}}_{q}\left(\Sigma \right)$, where $\Sigma$ is a punctured surface of genus $g>0$ and $q$ is an $N$-th root of unity with $N$ odd. As an application, we construct a family of representations of the Kauffman bracket skein algebra of the closed surface $\overline{\Sigma }$.

##### Keywords
quantum Teichmüller theory, skein algebras, quantum topology
##### Mathematical Subject Classification 2010
Primary: 20G42, 57M50, 57R56