Jacobi polynomials and SU(2,2)

2013/07/28 by E. Celeghini, Celeghini, E., M. A. del Olmo +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #math-ph #math.GR #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1307.7380

18 pages, 2 figures

arxiv created 2013/07/28 · arxiv updated 2013/07/30

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 L² functions defined on (-1,+1) x Z x Z/2.

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