The Gel’fand realization and the generating function of the Clebsch–Gordan coefficients of SL(2,R) in the hyperbolic basis

DOI10.1063/1.527827zbMath0617.22019OpenAlexW2004818095MaRDI QIDQ4726483

Debabrata Basu

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1063/1.527827

zbMATH Keywords

generating functionClebsch-Gordan coefficientshypergeometric equationhyperbolic basisSO(2)SL(2, \({bbfR})\)

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70) Semisimple Lie groups and their representations (22E46)

Related Items (1)

The Clebsch–Gordan problem of the SL(2,R) coherent states

Cites Work

• Complex angular momenta and the groups \(\mathrm{SU}(1,1)\) and \(\mathrm{SU}(2)\)
• The master analytic function and the Lorentz group. III. Coupling of continuous representations of O(2,1)
• The Gel’fand realization and the exceptional representations of SL(2,R)
• On the Kronecker Products of Irreducible Representations of the 2 × 2 Real Unimodular Group. I
• The Clebsch–Gordan coefficients of the three-dimensional Lorentz algebra in the parabolic basis
• Some new identities of the Clebsch–Gordan coefficients and representation functions of SO(2,1) and SO(4)
• Note on the representation spaces of O(2,1)
• Clebsch-Gordan problem and coefficients for the three-dimensional Lorentz group in a continuous basis. I
• On the wigner coefficients of the three-dimensional Lorentz group
• EXPANSIONS OF HYPERGEOMETRIC FUNCTIONS

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