JournalsqtVol. 4 , No. 3pp. 303–351

On the SL(2,ℂ) quantum 6<var>j</var>-symbols and their relation to the hyperbolic volume

  • Francesco Costantino

    IRMA, Strasbourg, France
  • Jun Murakami

    Waseda University, Tokyo, Japan
On the SL(2,ℂ) quantum 6<var>j</var>-symbols and their relation to the hyperbolic volume cover
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Abstract

We generalize the colored Alexander invariant of knots to an invariant of graphs and we construct a face model for this invariant by using the corresponding 6j6j-symbols, which come from the non-integral representations of the quantum group Uq(sl2){\mathcal U}_q(\mathrm{sl}_2). We call it the SL(2,C)\mathrm{SL}(2, \mathbb C)-quantum 6j6j-symbols, and show their relation to the hyperbolic volume of a truncated tetrahedron.

Cite this article

Francesco Costantino, Jun Murakami, On the SL(2,ℂ) quantum 6<var>j</var>-symbols and their relation to the hyperbolic volume. Quantum Topol. 4 (2013), no. 3 pp. 303–351

DOI 10.4171/QT/41