The Gel’fand realization and the exceptional representations of SL(2,R)

DOI10.1063/1.526799zbMath0556.22012OpenAlexW2011101629MaRDI QIDQ3220778

Tanmoy Bhattacharya, Debabrata Basu

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1063/1.526799

zbMATH Keywords

exceptional representationsSL(2,R)Gel'fand-Graev-Vilenkin realization

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Semisimple Lie groups and their representations (22E46)

Related Items (2)

Development of Linear Canonical Transforms: A Historical Sketch ⋮ The Gel’fand realization and the generating function of the Clebsch–Gordan coefficients of SL(2,R) in the hyperbolic basis

Cites Work

• Complex angular momenta and the groups \(\mathrm{SU}(1,1)\) and \(\mathrm{SU}(2)\)
• Matrix elements of representations of noncompact groups in a continuous basis
• The Plancherel formula for the universal covering group of SL(R, 2)
• Irreducible unitary representations of the Lorentz group
• The master analytic function and the Lorentz group. III. Coupling of continuous representations of O(2,1)
• Canonical transforms. IV. Hyperbolic transforms: Continuous series of SL(2,R) representations
• Noncompact Lie-algebraic approach to the unitary representations of SU∼(1,1): Role of the confluent hypergeometric equation
• The unitary irreducible representations of SL(2, R) in all subgroup reductions
• On non-compact groups. II. Representations of the 2+1 Lorentz group
• Uniformly bounded representations of the universal covering group of ${\text{SL}}\left( {2,\,R} \right)$
• Master Analytic Representation: Reduction of O(2, 1) in an O(1, 1) Basis
• Group Representation in a Continuous Basis: An Example
• Matrices of Finite Lorentz Transformations in a Noncompact Basis. I. Discrete Series of O(2, 1)
• New forms for the representations of the three-dimensional Lorentz group
• Mixed basis matrix elements for the subgroup reductions of SO(2,1)

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