Irreducible decomposition for local representations of quantum Teichmüller space

Jérémy Toulisse

Vol. 294 (2018), No. 1, 233–256

DOI: 10.2140/pjm.2018.294.233

Abstract

We give an irreducible decomposition of the so-called local representations (Bai, Bonahon and Liu, 2007) of the quantum Teichmüller space ${\mathcal{T}}_q\left(\Sigma \right)$, 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

Milestones

Received: 12 October 2016

Revised: 1 March 2017

Accepted: 28 April 2017

Published: 5 January 2018