Generating functions for orthogonal polynomials of \(A_{2}\), \(C_{2}\) and \(G_{2}\)

DOI10.3390/sym10080354zbMath1423.33023OpenAlexW2888198354MaRDI QIDQ2333662

Tomasz Czyżycki, Jiří Hrivnák, Jirí Patera

Publication date: 13 November 2019

Published in: Symmetry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/sym10080354

zbMATH Keywords

Weyl groupLie algebragenerating functionroot systemorthogonal polynomial

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Connections of hypergeometric functions with groups and algebras, and related topics (33C80)

Related Items (1)

Discrete cosine and sine transforms generalized to honeycomb lattice II. Zigzag boundaries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generating functions of Chebyshev polynomials in three variables
• Discrete Fourier analysis and Chebyshev polynomials with \(G_{2}\) group
• Gaussian cubature arising from hybrid characters of simple Lie groups
• Cubature formulae for orthogonal polynomials in terms of elements of finite order of compact simple Lie groups
• The generating function of bivariate Chebyshev polynomials associated with the Lie algebra \(G_2\)
• Orthogonality within the families of \(C\)-, \(S\)-, and \(E\)-functions of any compact semisimple Lie group
• Antisymmetric orbit functions
• Orbit functions
• Generating-function method for tensor products
• Weight-lattice discretization of Weyl-orbit functions
• On discretization of tori of compact simple Lie groups: II
• Generalized discrete orbit function transforms of affine Weyl groups
• On Multivariate Chebyshev Polynomials and Spectral Approximations on Triangles
• Standard Young tableaux and character generators of classical Lie groups
• Discrete Fourier Analysis, Cubature, and Interpolation on a Hexagon and a Triangle
• Discrete and continuous cosine transform generalized to Lie groups SU(2)×SU(2) and O(5)
• On discretization of tori of compact simple Lie groups
• Character generators for unitary and symplectic groups
• The character generator of SU(n)
• Generalized SU(2) spherical harmonics
• Generalized Chebyshev Polynomials Associated with Affine Weyl Groups
• On calculation of generating functions of Chebyshev polynomials in several variables
• On character generators for simple Lie algebras
• Reflection groups and invariant theory

This page was built for publication: Generating functions for orthogonal polynomials of \(A_{2}\), \(C_{2}\) and \(G_{2}\)