Quantum Teichmüller spaces and Kashaev's 6j-symbols
arXiv:0706.2026
Abstract
The Kashaev invariants of 3-manifolds are based on -symbols from the representation theory of the Weyl algebra, a Hopf algebra corresponding to the Borel subalgebra of $U_q(sl(2,\C))$. In this paper, we show that Kashaev's -symbols are intertwining operators of local representations of quantum Teichmüller spaces. This relates Kashaev's work with the theory of quantum Teichmüller space, which was developed by Chekhov-Fock, Kashaev and continued by Bonahon-Liu.
18 pages, 2 figures