SU(2), Associated Laguerre Polynomials and Rigged Hilbert Spaces

  • Enrico Celeghini
  • Manuel Gadella
  • Mariano A. del OlmoEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 255)


We present a family of unitary irreducible representations of SU(2) realized in the plane, in terms of the associated Laguerre polynomials. These functions are similar to the spherical harmonics defined on the sphere. Relations with a space of square integrable functions defined on the plane, \(L^2({\mathbb R}^2)\), are analyzed. We have also enlarged this study using rigged Hilbert spaces that allow to work with discrete and continuous bases like is the case here.


Lie group representations Special functions Rigged Hilbert spaces 



Partial financial support is acknowledged to the Junta de Castilla y León and FEDER (Project VA057U16) and MINECO of Spain (Project MTM2014-57129-C2-1-P).


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  • Enrico Celeghini
    • 1
    • 2
  • Manuel Gadella
    • 3
  • Mariano A. del Olmo
    • 3
    Email author
  1. 1.Dpto di FisicaUniversità di Firenze and INFN–Sezione di FirenzeFirenzeItaly
  2. 2.Dpto. de Física TeóricaUniversidad de ValladolidValladolidSpain
  3. 3.Dpto de Física Teórica and IMUVAUniv. de ValladolidValladolidSpain

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