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

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

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

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

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

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

1990, ISBN 9789810202835, 322

Book

Annals of Physics, ISSN 0003-4916, 08/2015, Volume 359, pp. 252 - 289

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the...

[formula omitted] Wigner–Racah algebra | Bivariate Gaussian | Finite many-particle quantum systems | Transition strengths | Embedded ensembles | Bivariate moments | U(N) Wigner-Racah algebra | PHYSICS, MULTIDISCIPLINARY | INTERACTING PARTICLE-SYSTEMS | U (N) Wigner-Racah algebra | SPECTRAL PROPERTIES | CE ATOM | DISTRIBUTIONS | CHAOS | PARITY | NUCLEI | STATISTICAL SPECTROSCOPY | GAUSSIAN ENSEMBLES | COEFFICIENTS | Specific gravity | Analysis | Algebra | Matrix | Random variables | Finite element analysis | Theory | Density | Quantum physics

[formula omitted] Wigner–Racah algebra | Bivariate Gaussian | Finite many-particle quantum systems | Transition strengths | Embedded ensembles | Bivariate moments | U(N) Wigner-Racah algebra | PHYSICS, MULTIDISCIPLINARY | INTERACTING PARTICLE-SYSTEMS | U (N) Wigner-Racah algebra | SPECTRAL PROPERTIES | CE ATOM | DISTRIBUTIONS | CHAOS | PARITY | NUCLEI | STATISTICAL SPECTROSCOPY | GAUSSIAN ENSEMBLES | COEFFICIENTS | Specific gravity | Analysis | Algebra | Matrix | Random variables | Finite element analysis | Theory | Density | Quantum physics

Journal Article

Annals of Physics, ISSN 0003-4916, 11/2010, Volume 325, Issue 11, pp. 2451 - 2485

Form fermions in Ω number of single particle orbitals, each fourfold degenerate, we introduce and analyze in detail embedded Gaussian unitary ensemble of...

Finite interacting Fermi systems | Embedded ensembles | Cross-correlations | Racah coefficients | Spectral variances | EGUE-SU | U(N) RACAH COEFFICIENTS | NUCLEAR-SPECTRA | SPIN | PHYSICS, MULTIDISCIPLINARY | INTERACTING PARTICLE-SYSTEMS | TENSOR OPERATORS | MODEL | DISTRIBUTIONS | STATISTICAL PROPERTIES | MANY-BODY SYSTEMS | QUANTUM CHAOS | Mathematics | Algebra | Matrix | Particle physics | Fermions | Mathematical analysis | Images | Centroids | Matrices | Spectra | Symmetry | RANDOMNESS | VARIATIONS | RACAH COEFFICIENTS | MATHEMATICAL OPERATORS | CORRELATIONS | FERMI GAS MODEL | ENERGY LEVELS | PARTICLE PROPERTIES | IRREDUCIBLE REPRESENTATIONS | PERIODICITY | MATHEMATICS | ANGULAR MOMENTUM | TWO-BODY PROBLEM | SCALARS | LIE GROUPS | QUANTUM OPERATORS | HAMILTONIANS | SU GROUPS | ALGEBRA | MANY-BODY PROBLEM | MATHEMATICAL MODELS | SYMMETRY GROUPS | MATRIX ELEMENTS | NUCLEAR MODELS | SU-4 GROUPS | NUCLEAR PHYSICS AND RADIATION PHYSICS | NUCLEI | MATRICES | NUCLEAR STRUCTURE | GROUND STATES

Finite interacting Fermi systems | Embedded ensembles | Cross-correlations | Racah coefficients | Spectral variances | EGUE-SU | U(N) RACAH COEFFICIENTS | NUCLEAR-SPECTRA | SPIN | PHYSICS, MULTIDISCIPLINARY | INTERACTING PARTICLE-SYSTEMS | TENSOR OPERATORS | MODEL | DISTRIBUTIONS | STATISTICAL PROPERTIES | MANY-BODY SYSTEMS | QUANTUM CHAOS | Mathematics | Algebra | Matrix | Particle physics | Fermions | Mathematical analysis | Images | Centroids | Matrices | Spectra | Symmetry | RANDOMNESS | VARIATIONS | RACAH COEFFICIENTS | MATHEMATICAL OPERATORS | CORRELATIONS | FERMI GAS MODEL | ENERGY LEVELS | PARTICLE PROPERTIES | IRREDUCIBLE REPRESENTATIONS | PERIODICITY | MATHEMATICS | ANGULAR MOMENTUM | TWO-BODY PROBLEM | SCALARS | LIE GROUPS | QUANTUM OPERATORS | HAMILTONIANS | SU GROUPS | ALGEBRA | MANY-BODY PROBLEM | MATHEMATICAL MODELS | SYMMETRY GROUPS | MATRIX ELEMENTS | NUCLEAR MODELS | SU-4 GROUPS | NUCLEAR PHYSICS AND RADIATION PHYSICS | NUCLEI | MATRICES | NUCLEAR STRUCTURE | GROUND STATES

Journal Article

Ramanujan Journal, ISSN 1382-4090, 06/2017, Volume 43, Issue 2, pp. 243 - 311

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

Algebra | Fermions | Asymptotic properties | Mathematical analysis | Mathematical models | Racah coefficient | Bosons | Symmetry

Conference Proceeding

11.
Wigner-Racah algebra, binary correlations and trace propagation for embedded random matrix ensembles

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

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

Eigenvectors of the tridiagonal matrices of Sylvester type are explicitly determined. These are closely related to orthogonal polynomials named after...

Krawtchouk polynomial | Secondary 65F15 | Mathematics | Theory of Computation | Primary 15A18 | eigenvector | q -Racah polynomial | Racah polynomial | Numerical Analysis | dual Hahn polynomial | Tridiagonal matrix | Sylvester determinant | eigenvalue | Eigenvector | Eigenvalue | Q-Racah polynomial | Dual Hahn polynomial | MATHEMATICS | q-Racah polynomial | Polynomials | Matrix | Numerical analysis

Krawtchouk polynomial | Secondary 65F15 | Mathematics | Theory of Computation | Primary 15A18 | eigenvector | q -Racah polynomial | Racah polynomial | Numerical Analysis | dual Hahn polynomial | Tridiagonal matrix | Sylvester determinant | eigenvalue | Eigenvector | Eigenvalue | Q-Racah polynomial | Dual Hahn polynomial | MATHEMATICS | q-Racah polynomial | Polynomials | Matrix | Numerical analysis

Journal Article

Computer Physics Communications, ISSN 0010-4655, 2006, Volume 174, Issue 8, pp. 616 - 630

The Wigner D-functions, D p q j ( α , β , γ ) , are known for their frequent use in quantum mechanics. Defined as the matrix elements of the rotation operator...

Wigner D-function and rotation matrix | Wigner [formula omitted] symbol | Angular momentum | Finite rotation matrix | Reduced rotation matrix | Clebsch–Gordan expansion | Racah algebra techniques | Wigner j symbol | Clebsch-Gordan expansion | ELEMENTS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Racah algebra tcchniques | reduced rotation matrix | Wigner n - j symbol | angular momentum | COMPUTATIONS | PHYSICS, MATHEMATICAL | REAL SPHERICAL-HARMONICS | finite rotation matrix

Wigner D-function and rotation matrix | Wigner [formula omitted] symbol | Angular momentum | Finite rotation matrix | Reduced rotation matrix | Clebsch–Gordan expansion | Racah algebra techniques | Wigner j symbol | Clebsch-Gordan expansion | ELEMENTS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Racah algebra tcchniques | reduced rotation matrix | Wigner n - j symbol | angular momentum | COMPUTATIONS | PHYSICS, MATHEMATICAL | REAL SPHERICAL-HARMONICS | finite rotation matrix

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

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

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

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

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

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

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

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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