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racah coefficients (94) 94
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Journal of Approximation Theory, ISSN 0021-9045, 11/2015, Volume 199, pp. 1 - 12
For a one-parameter family of lower triangular matrices with entries involving continuous q-ultraspherical polynomials we give an explicit lower triangular... 
Continuous [formula omitted]-ultraspherical polynomials | [formula omitted]-Racah polynomials | Orthogonal polynomials | [formula omitted]-analogues | Q-Racah polynomials | Continuous q-ultraspherical polynomials | Q-analogues | MATHEMATICS | q-Racah polynomials | q-analogues
Journal Article
Modern Physics Letters A, ISSN 0217-7323, 02/2018, Volume 33, Issue 4, p. 1850020
One of the spectacular results in mathematical physics is the expression of Racah matrices for symmetric representations of the quantum group SUq(2) through... 
differential expansion | knot polynomials | Racah matrices | POLYNOMIAL INVARIANT | EVOLUTION | ASTRONOMY & ASTROPHYSICS | HECKE ALGEBRA | PHYSICS, NUCLEAR | DIFFERENTIAL HIERARCHY | PHYSICS, MATHEMATICAL | KNOTS | PHYSICS, PARTICLES & FIELDS
Journal Article
International Journal of Modern Physics A, ISSN 0217-751X, 06/2018, Volume 33, Issue 17, p. 1850105
Quantum ℛ -matrices are the building blocks for the colored HOMFLY polynomials. In the case of three-strand braids with an identical finite-dimensional... 
representation theory | knot theory | Racah matrices | Chern-Simons theory | quantum groups | topological field theory | COLORED KNOT POLYNOMIALS | REPRESENTATIONS | FIELD-THEORIES | INVARIANTS | LINKS | PHYSICS, NUCLEAR | PRETZEL KNOTS | ALGEBRAS | EVOLUTION | PHYSICS, PARTICLES & FIELDS | Physics - High Energy Physics - Theory
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 10/2018, Volume 132, pp. 155 - 180
This paper is a next step in the project of systematic description of colored knot and link invariants started in Mironov and Morozov (2015) and Mironov et al.... 
Chern-Simons theory | Racah coefficients | Link invariants | MATHEMATICS | EVOLUTION | FIELD-THEORY | PROOF | PHYSICS, MATHEMATICAL | KNOT POLYNOMIALS
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 09/2009, Volume 42, Issue 35, pp. 353001 - 353001 (28)
The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combining angular momentum theory... 
PHASE | SYMMETRY | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | RACAH ALGEBRA | LINE | QUANTUM-SYSTEMS | MEAN KINGS PROBLEM | PHYSICS, MATHEMATICAL | WIGNER | OPERATORS | Physics - Quantum Physics | Quantum Physics | Physics
Journal Article
Journal of Physics: Conference Series, ISSN 1742-6588, 2014, Volume 538, Issue 1, pp. 1 - 12
Random matrix ensembles for a system of m number of fermions or bosons in [Omega] number of single particle levels each r-fold degenerate and interacting with... 
Algebra | Fermions | Asymptotic properties | Mathematical analysis | Mathematical models | Racah coefficient | Bosons | Symmetry
Conference Proceeding
Journal of Physics: Conference Series, ISSN 1742-6588, 2012, Volume 403, Issue 1, pp. 1 - 7
For embedded unitary ensembles with SU([Omega]) x SU(r) embedding and generated by random two-body (in some situations k-body) interactions preserving SU(r)... 
Correlation | Approximation | Fermions | Mathematical analysis | Eigenvalues | Gaussian | Binary systems (materials) | Density | Racah coefficient
Conference Proceeding
Calcolo, ISSN 0008-0624, 12/2008, Volume 45, Issue 4, pp. 217 - 233
Journal Article
Computer Physics Communications, ISSN 0010-4655, 2006, Volume 174, Issue 8, pp. 616 - 630
Journal Article
Reviews in Mathematical Physics, ISSN 0129-055X, 07/2018, Volume 30, Issue 6, p. 1840005
This is a review of ( q -)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable... 
UNITARY REPRESENTATIONS | DISCRETE LIOUVILLE THEORY | INVARIANTS | QUANTUM | CHERN-SIMONS THEORY | MATRIX MODELS | CONFORMAL BLOCKS | PHYSICS, MATHEMATICAL | OPERATORS | KNOTS | RACAH MATRICES
Journal Article
International Journal of Modern Physics A, ISSN 0217-751X, 09/2015, Volume 30, Issue 26, p. 1550169
This paper starts a systematic description of colored knot polynomials, beginning from the first non-(anti)symmetric representation R = [ 2 , 1 ] . The project... 
knot invariants | Chern-Simons theory | Racah matrices | INVARIANTS | PHYSICS, NUCLEAR | MATRIX MODELS | DIFFERENTIAL HIERARCHY | HOMOLOGY | PHYSICS, PARTICLES & FIELDS
Journal Article
PHYSICS OF PARTICLES AND NUCLEI, ISSN 1063-7796, 03/2020, Volume 51, Issue 2, pp. 172 - 219
We try to present on the elementary level a popular subject of the mathematical physics. The subject begins with the famous paper by E. Witten "Quantum field... 
VASSILIEV INVARIANTS | FIELD-THEORY | BRAIDS | ALGEBRA | EXPANSION | ANYONS | CHERN-SIMONS THEORY | EQUATIONS | QUANTUM RACAH MATRICES | MODEL | PHYSICS, PARTICLES & FIELDS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2016, Volume 433, Issue 1, pp. 525 - 542
In this paper we provide properties—which are, to the best of our knowledge, new—of the zeros of the polynomials belonging to the q-Askey scheme. These... 
q-Racah polynomials | Diophantine relations | Isospectral matrices | q-Askey scheme | Zeros of polynomials | Askey–Wilson polynomials | Q-Askey scheme | Askey-Wilson polynomials | Q-Racah polynomials | MATHEMATICS | MATHEMATICS, APPLIED | TRIDIAGONAL MATRICES | ORTHOGONAL POLYNOMIALS | SUM | DIOPHANTINE PROPERTIES
Journal Article
JETP Letters, ISSN 0021-3640, 11/2018, Volume 108, Issue 10, pp. 697 - 704
In the present paper, we discuss the eigenvalue conjecture, suggested in 2012, in the particular case of U-q(sl(N)) 6-j The eigenvalue conjecture provides a... 
QUANTUM RACAH MATRICES | ALGEBRAS | PHYSICS, MULTIDISCIPLINARY | INVARIANTS | KNOT POLYNOMIALS
Journal Article
Modern Physics Letters A, ISSN 0217-7323, 04/2018, Volume 33, Issue 12, p. 1850062
Factorization of the differential expansion (DE) coefficients for colored HOMFLY-PT polynomials of antiparallel double braids, originally discovered for... 
colored knot polynomials | non-rectangular representations | Racah matrices | POLYNOMIAL INVARIANT | MATRIX FACTORIZATIONS | FIELD-THEORY | PHYSICS, NUCLEAR | KNOT INVARIANTS | PHYSICS, MATHEMATICAL | LINK HOMOLOGY | ASTRONOMY & ASTROPHYSICS | EXCEPTIONAL SERIES | PHYSICS, PARTICLES & FIELDS
Journal Article
Physics Letters B, ISSN 0370-2693, 03/2018, Volume 778, Issue C, pp. 197 - 206
The differential expansion is one of the key structures reflecting group theory properties of colored knot polynomials, which also becomes an important tool... 
EVOLUTION | FIELD-THEORY | INVARIANTS | ASTRONOMY & ASTROPHYSICS | PHYSICS, NUCLEAR | KNOT POLYNOMIALS | RACAH MATRICES | PHYSICS, PARTICLES & FIELDS | Geometric Topology | Mathematics - Quantum Algebra | Mathematics - Geometric Topology | Mathematics | High Energy Physics - Theory | Physics
Journal Article
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