Quantum Teichmüller spaces and Kashaev's 6j-symbols

2007/06/14 by Hua Bai, Bai, Hua
Mathematics · #20G42 #57R56 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA #msc:20G42 #msc:57R56

paper · pdf · doi:10.48550/arxiv.0706.2026

18 pages, 2 figures

arxiv created 2007/06/14 · arxiv updated 2009/12/01

Abstract

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 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.

Related

• A survey of quantum Teichmüller space and Kashaev algebra
• Local representations of the quantum Teichmuller space
• Intertwining operators of the quantum Teichmüller space
• Cyclic quantum Teichmüller theory
• Infinite-dimensional representations of U_q(\mathfraksl₂) and the shadow world: quantum 6j-symbols for Verma modules