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

Journal Article · Thu May 01 04:00:00 EDT 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531984· OSTI ID:544544

Van der Jeugt, J ^[1]

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1. Department of Applied Mathematics and Computer Science, University of Ghent, Krijgslaan 281-S9, B-9000 Gent (Belgium)

Representations of the Lie algebra su(1,1) and of a generalization of the oscillator algebra, b(1), are considered. The paper then introduces polynomials which are related by the coupling (or Clebsch{endash}Gordan) coefficients of the Lie algebra in question; by making a proper choice, these polynomials themselves are related to known special functions. The coupling of two or three representations of the Lie algebra then leads to interesting addition formulas for these special functions. The polynomials appearing here are generalized Laguerre and Jacobi polynomials for the su(1,1) case, and Hermite polynomials for the b(1) algebra. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 544544
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 5 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ALGEBRA
CLEBSCH-GORDAN COEFFICIENTS
COUPLING
FUNCTIONS
HERMITE POLYNOMIALS
IRREDUCIBLE REPRESENTATIONS
LIE GROUPS
POLYNOMIALS
QUANTUM MECHANICS
SU GROUPS