Jacobi polynomials and SU(2,2)
Mathematical Physics
2013-07-30 v1 Group Theory
math.MP
Quantum Physics
Abstract
A ladder structure of operators is presented for the Jacobi polynomials, J_n^(a,b)(x), with parameters n, a and b integers, showing that they are related to the unitary irreducible representation of SU(2,2) with quadratic Casimir C_SU(2,2)=-3/2. As they determine also a base of square-integrable functions, the universal enveloping algebra of su(2,2) is homomorphic to the space of linear operators acting on the L^2 functions defined on (-1,+1) x Z x Z/2.
Keywords
Cite
@article{arxiv.1307.7380,
title = {Jacobi polynomials and SU(2,2)},
author = {E. Celeghini and M. A. del Olmo and M. A. Velasco},
journal= {arXiv preprint arXiv:1307.7380},
year = {2013}
}
Comments
18 pages, 2 figures