Irreducible decomposition for local representations of quantum Teichmüller space

Abstract

We give an irreducible decomposition of the so-called local representations (see arXiv:0707.2151) of the quantum Teichmüller space ${\mathcal{T}}_q(\Sigma )$ where $\Sigma$ is a punctured surface of genus $g>0$ and $q$ is a primitive $N$-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 $\overline{\Sigma }$.

Now ready for publication

References in corpus (1)

• On Kauffman Bracket Skein Modules at Root of Unity