Geodesic
On the colored Jones polynomial and the Kashaev invariant
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 5, pp. 57-78

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We express the colored Jones polynomial as the inverse of the quantum determinant of a matrix with entries in the $q$-Weyl algebra of $q$-operators, evaluated at the trivial function (plus simple substitutions). The Kashaev invariant is proved to be equal to another special evaluation of the determinant. We also discuss the similarity between our determinant formula of the Kashaev invariant and the determinant formula of the hyperbolic volume of knot complements, hoping it would lead to a proof of the volume conjecture. 
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     author = {Huynh Vu and Le Tu Quoc Thang},
     title = {On the colored {Jones} polynomial and the {Kashaev} invariant},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {57--78},
     publisher = {mathdoc},
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     number = {5},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2005_11_5_a4/}
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Huynh Vu; Le Tu Quoc Thang. On the colored Jones polynomial and the Kashaev invariant. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 5, pp. 57-78. http://geodesic.mathdoc.fr/item/FPM_2005_11_5_a4/