576 research outputs found
On beta pentagon relations
The (quantum) pentagon relation underlies the existing constructions of three
dimensional quantum topology in the combinatorial framework of triangulations.
Following the recent works \cite{KashaevLuoVartanov2012,AndersenKashaev2013},
we discuss a special type of integral pentagon relations and their
relationships with the Faddeev type operator pentagon relations.Comment: 11 pages, Theorem 2 generalized to arbitrary LCA groups and
renumbered to Theorem
Proof of the volume conjecture for Whitehead doubles of a family of torus knots
A technique to calculate the colored Jones polynomials of satellite knots,
illustrated by the Whitehead doubles of knots, is presented. Then we prove the
volume conjecture for Whitehead doubles of a family of torus knots and show
some interesting observations.Comment: 18 pages, 3 figure
On the spectrum of Dehn twists in quantum Teichmuller theory
The operator realizing a Dehn twist in quantum Teichmuller theory is
diagonalized and continuous spectrum is obtained. This result is in agreement
with the expected spectrum of conformal weights in quantum Liouville theory at
c>1. The completeness condition of the eigenvectors includes the integration
measure which appeared in the representation theoretic approach to quantum
Liouville theory by Ponsot and Teschner. The underlying quantum group structure
is also revealed.Comment: 13 pages,8 figures,LaTeX2
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