133 citations · 885 across the 25 of their papers we have counts for
17 papers · 1 filter
Vogel's universality and the classification problem for Jacobi identities
A. Morozov, A. Sleptsov
This paper is a summary of discussions at the recent ITEP-JINR-YerPhI workshop on Vogel theory in Dubna. We consider relation between Vogel divisor(s) and the old Dynkin classifica…
Quantum Racah matrices up to level 3 and multicolored link invariants
C. Bai, J. Jiang, J. Liang +4
This paper is a next step in the project of systematic description of colored knot and link invariants started in previous papers. In this paper, we managed to explicitly find the…
On the block structure of the quantum R-matrix in the three-strand braids
L. Bishler, An. Morozov, A. Sleptsov +1
Quantum -matrices are the building blocks for the colored HOMFLY polynomials. In the case of three-strand braids with an identical finite-dimensional irreducible repre…
Eigenvalue hypothesis for multi-strand braids
Saswati Dhara, A. Mironov, A. Morozov +4
Computing polynomial form of the colored HOMFLY-PT for non-arborescent knots obtained from three or more strand braids is still an open problem. One of the efficient methods sugges…
Towards topological quantum computer
D. Melnikov, A. Mironov, S. Mironov +2
One of the principal obstacles on the way to quantum computers is the lack of distinguished basis in the space of unitary evolutions and thus the lack of the commonly accepted set…
Checks of integrality properties in topological strings
A. Mironov, A. Morozov, An. Morozov +3
Tests of the integrality properties of a scalar operator in topological strings on a resolved conifold background or orientifold of conifold backgrounds have been performed for arb…
Quantum Racah matrices and 3-strand braids in irreps R with |R|=4
A. Mironov, A. Morozov, An. Morozov +1
We describe the inclusive Racah matrices for the first non-(anti)symmetric rectangular representation R=[2,2] for quantum groups U_q(sl_N). Most of them have sizes 2, 3, and 4 and…
HOMFLY polynomials in representation [3,1] for 3-strand braids
A. Mironov, A. Morozov, An. Morozov +1
This paper is a new step in the project of systematic description of colored knot polynomials started in arXiv:1506.00339. In this paper, we managed to explicitly find the inclusiv…
Tabulating knot polynomials for arborescent knots
A. Mironov, A. Morozov, An. Morozov +3
Arborescent knots are the ones which can be represented in terms of double fat graphs or equivalently as tree Feynman diagrams. This is the class of knots for which the present kno…
Colored knot polynomials. HOMFLY in representation [2,1]
A. Mironov, A. Morozov, An. Morozov +1
This paper starts a systematic description of colored knot polynomials, beginning from the first non-(anti)symmetric representation R=[2,1]. The project involves several steps: (i)…
Colored HOMFLY polynomials for the pretzel knots and links
A. Mironov, A. Morozov, A. Sleptsov
With the help of the evolution method we calculate all HOMFLY polynomials in all symmetric representations [r] for a huge family of (generalized) pretzel links, which are made from…
Evolution method and HOMFLY polynomials for virtual knots
Ludmila Bishler, Alexei Morozov, Andrey Morozov +1
Following the suggestion of arXiv:1407.6319 to lift the knot polynomials for virtual knots and links from Jones to HOMFLY, we apply the evolution method to calculate them for an in…
On colored HOMFLY polynomials for twist knots
A. Mironov, A. Morozov, An. Morozov
Recent results of J.Gu and H.Jockers provide the lacking initial conditions for the evolution method in the case of the first non-trivially colored HOMFLY polynomials H_{[21]} for…
Racah coefficients and extended HOMFLY polynomials for all 5-, 6- and 7-strand braids
A. Anokhina, A. Mironov, A. Morozov +1
Basing on evaluation of the Racah coefficients for SU_q(3) (which supported the earlier conjecture of their universal form) we derive explicit formulas for all the 5-, 6- and 7-str…
Character expansion for HOMFLY polynomials. III. All 3-Strand braids in the first symmetric representation
H. Itoyama, A. Mironov, A. Morozov +1
We continue the program of systematic study of extended HOMFLY polynomials. Extended polynomials depend on infinitely many time variables, are close relatives of integrable tau-fun…
Torus HOMFLY as the Hall-Littlewood Polynomials
A. Mironov, A. Morozov, Sh. Shakirov
We show that the HOMFLY polynomials for torus knots T[m,n] in all fundamental representations are equal to the Hall-Littlewood polynomials in representation which depends on m, and…
HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
H. Itoyama, A. Mironov, A. Morozov +1
Explicit answer is given for the HOMFLY polynomial of the figure eight knot in arbitrary symmetric representation R=[p]. It generalizes the old answers for p=1 and 2 and the…