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 Tq(Σ), where Σ 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 Σ¯.

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
Authors
Jérémy Toulisse
Department of Mathematics
University of Southern Califonia
Los Angeles, CA
United States