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Manuscript Title: Construction of SO(5) ⊃ SO(3) spherical harmonics and Clebsch-Gordan coefficients
Authors: M.A. Caprio, D.J. Rowe, T.A. Welsh
Program title: GammaHarmonic
Catalogue identifier: AECY_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 180(2009)1150
Programming language: Mathematica 6.
Computer: Any which support Mathematica.
Operating system: Any which support Mathematica; tested under Microsoft Windows XP and Linux.
Keywords: SO(5), spherical harmonics, Clebsch-Gordan coefficients, coupling coefficients, isoscalar factors, Bohr Hamiltonian, SU(1, 1) × SO(5) algebraic collective model.
PACS: 02.20.Qs, 02.70.-c, 21.60.Ev, 21.60.Fw.
Classification: 4.2.

Nature of problem:
Explicit construction of SO(5) ⊃ SO(3) spherical harmonics on S4. Evaluation of SO(3)-reduced matrix elements and SO(5) ⊃ SO(3) Clebsch-Gordan coefficients (isoscalar factors).

Solution method:
Construction of SO(5) ⊃ SO(3) spherical harmonics by orthonormalization, obtained from a generating set of functions, according to the method [1]. Matrix elements and Clebsch-Gordan coefficients follow by construction and integration of SO(3) scalar products.

Running time:
Depends strongly on the maximum SO(5) and SO(3) representation labels involved. A few minutes for the calculation in the Mathematica notebook.

[1] D. J. Rowe, P. S. Turner, and J. Repka (J. Math. Phys. 45 (2004) 2761).