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Jacobi Polynomials as su(2, 2) Unitary Irreducible Representation

  • Enrico Celeghini
  • Mariano A. del OlmoEmail author
  • Miguel A. Velasco
Chapter
Part of the CRM Series in Mathematical Physics book series (CRM)

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 dj-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.

Keywords

Jacobi polynomials Lie algebras Irreducible representations Wigner matrices Operators on special functions 

PACS

02.20.Sv 02.30Gp 03.65Db 

Mathematics Subject Classification (2000)

17B15 17B81 33C45 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Enrico Celeghini
    • 1
    • 2
  • Mariano A. del Olmo
    • 2
    Email author
  • Miguel A. Velasco
    • 3
  1. 1.Dpto di FisicaUniversità di Firenze and INFN–Sezione di FirenzeFirenzeItaly
  2. 2.Dpto de Física Teórica and IMUVAUniv. de ValladolidValladolidSpain
  3. 3.Departamento de Física Teórica, Atómica y ÓpticaUniversidad de ValladolidValladolidSpain

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