Abstract
An infinite-dimensional irreducible representation of su(2, 2) is explicitly constructed in terms of ladder operators for the Jacobi polynomials \(J_{n}^{({\alpha },\beta )}(x)\) and the Wigner d j-matrices where the integer and half-integer spins j := n + (α + β)∕2 are considered together. The 15 generators of this irreducible representation are realized in terms of zero or first order differential operators and the algebraic and analytical structure of operators of physical interest discussed.
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Acknowledgements
This research is supported in part by the Ministerio de Economía y Competitividad of Spain under grant MTM2014-57129-C2-1-P and the Junta de Castilla y León (Projects VA057U16, VA137G18, and BU229P18).
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Celeghini, E., del Olmo, M.A., Velasco, M.A. (2019). Jacobi Polynomials as su(2, 2) Unitary Irreducible Representation. In: Kuru, Ş., Negro, J., Nieto, L. (eds) Integrability, Supersymmetry and Coherent States. CRM Series in Mathematical Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-20087-9_10
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