Coupling coefficients for Lie algebra representations and addition formulas for special functions

DOI10.1063/1.531984zbMath0897.17005OpenAlexW2148677738WikidataQ115329142 ScholiaQ115329142MaRDI QIDQ4345119

Joris Van der Jeugt

Publication date: 11 October 1998

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531984

zbMATH Keywords

representationsJacobi polynomialsHermite polynomialscoupling coefficientsgeneralized Laguerre polynomialsaddition formulasgeneralized oscillator algebra \(b(1)\)Lie algebras \(su(1.1)\)

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Representations of Lie algebras and Lie superalgebras, analytic theory (17B15) Spherical harmonics (33C55)

Related Items (17)

Expansion formulas for terminating balanced \(_{4} F_{3}\)-series from the Biedenharn--Elliot identity for \(\mathfrak{su}(1,1)\) ⋮ su(1,1) intelligent states ⋮ The Racah algebra: An overview and recent results ⋮ Coupling coefficients for tensor product representations of quantum SU(2) ⋮ 3nj-coefficients of su(1,1) as connection coefficients between orthogonal polynomials in n variables ⋮ Matrix elements of SO(3) in sl3 representations as bispectral multivariate functions ⋮ Realisations of Racah algebras using Jacobi operators and convolution identities ⋮ Realizations of coupled vectors in the tensor product of representations of \(\mathfrak{su}(1,1)\) and \(\mathfrak{su}(2)\) ⋮ Racah problems for the oscillator algebra, the Lie algebra \(\mathfrak{sl}_n\), and multivariate Krawtchouk polynomials ⋮ Inequalities for zeros of Jacobi polynomials via Obrechkoff’s theorem ⋮ Transformation brackets between U(N)⊃SO(N)⊃SO(Na)⊕SO(Nb) and U(N)⊃U(Na)⊕U(Nb)⊃SO(Na)⊕SO(Nb) ⋮ Convolutions and zeros of orthogonal polynomials ⋮ Generating function for the Bannai-Ito polynomials ⋮ Realizations of su(1,1) and Uq(su(1,1)) and generating functions for orthogonal polynomials ⋮ Convolution identities for Dunkl orthogonal polynomials from the osp(1|2) Lie superalgebra ⋮ Hypergeometric series related to the \(9-j\) coefficient of \({\mathfrak{su}}(1,1)\) ⋮ SU(3) Clebsch–Gordan coefficients and some of their symmetries

Cites Work

• New construction of 3nj-symbols
• A unitary representation of SL(2,R)

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