https://doi.org/10.1140/epjc/s10052-018-5765-5
Regular Article - Theoretical Physics
Eigenvalue conjecture and colored Alexander polynomials
1
Lebedev Physics Institute, Moscow, 119991, Russia
2
ITEP, Moscow, 117218, Russia
3
Institute for Information Transmission Problems, Moscow, 127994, Russia
4
National Research Nuclear University MEPhI, Moscow, 115409, Russia
* e-mail: mironov@lpi.ru
** e-mail: mironov@itep.ru
Received:
19
October
2016
Accepted:
26
March
2018
Published online:
5
April
2018
We connect two important conjectures in the theory of knot polynomials. The first one is the property 
for all single hook Young diagrams R, which is known to hold for all knots. The second conjecture claims that all the mixing matrices 
in the relation 
between the ith and the first generators 
of the braid group are universally expressible through the eigenvalues of 
. Since the above property of Alexander polynomials is very well tested, this relation provides new support to the eigenvalue conjecture, especially for 
, when its direct check by evaluation of the Racah matrices and their convolutions is technically difficult.
© The Author(s), 2018
