Quantum Teichmüller spaces and Kashaev's 6j-symbols

Details Quantum Teichmüller spaces and Kashaev's 6j-symbols Quantum Teichmüller spaces and Kashaev's 6j-symbols

2007-06-14

arxiv.org/abs/0706.2026v1

Mathematics

Geometric Topology

18 pages, 2 figures

Scientific paper

The Kashaev invariants of 3-manifolds are based on $6j$-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 $6j$-symbols are intertwining operators of local representations of quantum Teichm\"uller spaces. This relates Kashaev's work with the theory of quantum Teichm\"uller space, which was developed by Chekhov-Fock, Kashaev and continued by Bonahon-Liu.

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