1971, The Appleton-Century mathematics series, 162

Book

2014, Second edition., Encyclopedia of mathematics and its applications, ISBN 1107071895, Volume 155, xvii, 420

Serving both as an introduction to the subject and as a reference, this book presents the theory in elegant form and with modern concepts and notation. It...

Functions of several real variables | Orthogonal polynomials

Functions of several real variables | Orthogonal polynomials

Book

1975, Lecture notes in mathematics, ISBN 9780387071329, Volume 435., vi, 181

Book

2001, Encyclopedia of mathematics and its applications, ISBN 0521800439, Volume 81., xv, 390

This is the first modern book on orthogonal polynomials of several variables, which are interesting both as objects of study and as tools used in multivariate...

Functions of several real variables | Orthogonal polynomials

Functions of several real variables | Orthogonal polynomials

Book

1984, Volume PM-R8406., 31

Book

Symmetry, ISSN 2073-8994, 2016, Volume 8, Issue 10, pp. 108 - 108

Harmonic polynomials of type A are polynomials annihilated by the Dunkl Laplacian associated to the symmetric group acting as a reflection group on R-N. The...

Harmonic polynomi | Symmetric group | Dunkl operators | symmetric group | MULTIDISCIPLINARY SCIENCES | harmonic polynomials | Harmonics | Operators | Computation | Gaussian | Polynomials | Reflection | Symmetry | Mathematics - Classical Analysis and ODEs

Harmonic polynomi | Symmetric group | Dunkl operators | symmetric group | MULTIDISCIPLINARY SCIENCES | harmonic polynomials | Harmonics | Operators | Computation | Gaussian | Polynomials | Reflection | Symmetry | Mathematics - Classical Analysis and ODEs

Journal Article

SYMMETRY-BASEL, ISSN 2073-8994, 04/2019, Volume 11, Issue 4, p. 503

For each partition of N, there are irreducible modules of the symmetric groups and of the corresponding Hecke algebra whose bases consist of the reverse...

singular values | Hecke algebra | nonsymmetric Jack and Macdonald polynomials | Young tableaux | MULTIDISCIPLINARY SCIENCES

singular values | Hecke algebra | nonsymmetric Jack and Macdonald polynomials | Young tableaux | MULTIDISCIPLINARY SCIENCES

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2018, Volume 14

There is a space of vector-valued nonsymmetric Jack polynomials associated with any irreducible representation of a symmetric group. Singular polynomials for...

Standard modules | Young tableaux | Nonsymmetric jack polynomials | PHYSICS, MATHEMATICAL | nonsymmetric Jack polynomials | standard modules | Polynomials | Mathematics - Representation Theory

Standard modules | Young tableaux | Nonsymmetric jack polynomials | PHYSICS, MATHEMATICAL | nonsymmetric Jack polynomials | standard modules | Polynomials | Mathematics - Representation Theory

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 03/2016, Volume 12

For each irreducible module of the symmetric group on [...] objects there is a set of parametrized nonsymmetric Jack polynomials in [...] variables taking...

Fourier-stieltjes coefficients | Matrix-valued measure | Nonsymmetric Jack polynomials | Symmetric group modules

Fourier-stieltjes coefficients | Matrix-valued measure | Nonsymmetric Jack polynomials | Symmetric group modules

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 05/2017, Volume 50, Issue 24, p. 245201

The Hamiltonian of the quantum Calogero-Sutherland model of N identical particles on the circle with 1/r(2) interactions has eigenfunctions consisting of Jack...

representations of the symmetric group | generalized Jack polynomials | Calogero-Sutherland model on torus | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

representations of the symmetric group | generalized Jack polynomials | Calogero-Sutherland model on torus | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL

Journal Article

Symmetry, ISSN 2073-8994, 10/2018, Volume 10, Issue 11, p. 541

We prove many factorization formulas for highest weight Macdonald polynomials indexed by particular partitions called quasistaircases. Consequently, we prove a...

Jack polynomials | Macdonald polynomials | Clustering properties | Quantum Hall theory | Highest weight polynomials | Quasistaircases factorizations | QUANTUM HALL STATES | quasistaircases factorizations | FLUID | AFFINE HECKE ALGEBRAS | MULTIDISCIPLINARY SCIENCES | highest weight polynomials | clustering properties | quantum Hall theory | OPERATORS | Combinatorics | Mathematics

Jack polynomials | Macdonald polynomials | Clustering properties | Quantum Hall theory | Highest weight polynomials | Quasistaircases factorizations | QUANTUM HALL STATES | quasistaircases factorizations | FLUID | AFFINE HECKE ALGEBRAS | MULTIDISCIPLINARY SCIENCES | highest weight polynomials | clustering properties | quantum Hall theory | OPERATORS | Combinatorics | Mathematics

Journal Article

2014, 2nd ed., Encyclopedia of Mathematics and its Applications, ISBN 9781107786134, Volume no. 155

Web Resource

2014, 2nd ed., Encyclopedia of Mathematics and its Applications, ISBN 9781107786134, Volume no. 155

Web Resource

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2013, Volume 9, p. 043

This is a sequel to [SIGMA 9 (2013), 007, 23 pages], in which there is a construction of a 2×2 positive-definite matrix function K(x) on R2. The entries of...

Matrix gaussian weight function | matrix Gaussian weight function

Matrix gaussian weight function | matrix Gaussian weight function

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 04/2014, Volume 10

The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for...

Standard module | Gaussian weight | Mathematics - Classical Analysis and ODEs

Standard module | Gaussian weight | Mathematics - Classical Analysis and ODEs

Journal Article

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 2013, Volume 9, p. 007

The structure of orthogonal polynomials on [...] with the weight function [...] is based on the Dunkl operators of type [...]. This refers to the full...

Harmonic polynomials | Matrix Gaussian weight function | matrix Gaussian weight function | harmonic polynomials

Harmonic polynomials | Matrix Gaussian weight function | matrix Gaussian weight function | harmonic polynomials

Journal Article

2014, Second edition., Encyclopedia of mathematics and its applications, ISBN 9781107071896, Volume 155

Web Resource

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), ISSN 1815-0659, 06/2017, Volume 13

For each irreducible module of the symmetric group S-N there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module....

Matrix-valued weight function | Nonsymmetric Jack polynomials | Symmetric group modules | REPRESENTATIONS | matrix-valued weight function | symmetric group modules | PHYSICS, MATHEMATICAL | nonsymmetric Jack polynomials | Operators (mathematics) | Toruses | Singularities | Mathematical analysis | Differential equations | Hyperplanes | Polynomials | Eigenvectors | Orthogonality | Mathematics - Classical Analysis and ODEs

Matrix-valued weight function | Nonsymmetric Jack polynomials | Symmetric group modules | REPRESENTATIONS | matrix-valued weight function | symmetric group modules | PHYSICS, MATHEMATICAL | nonsymmetric Jack polynomials | Operators (mathematics) | Toruses | Singularities | Mathematical analysis | Differential equations | Hyperplanes | Polynomials | Eigenvectors | Orthogonality | Mathematics - Classical Analysis and ODEs

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2012, Volume 45, Issue 9, p. 95305

Journal Article

RANDOM MATRICES-THEORY AND APPLICATIONS, ISSN 2010-3263, 10/2015, Volume 4, Issue 4

Two-qubit X-matrices have been the subject of considerable recent attention, as they lend themselves more readily to analytical investigations than two-qubit...

2 x 2 quantum systems | Peres-Horodecki conditions | separability probabilities | entanglement probability distribution | Hilbert-Schmidt measure | induced measure | STATISTICS & PROBABILITY | X-states | positive partial transpose | PHYSICS, MATHEMATICAL | continuous Dyson index

2 x 2 quantum systems | Peres-Horodecki conditions | separability probabilities | entanglement probability distribution | Hilbert-Schmidt measure | induced measure | STATISTICS & PROBABILITY | X-states | positive partial transpose | PHYSICS, MATHEMATICAL | continuous Dyson index

Journal Article

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