Lie groups, algebraic special functions and Jacobi polynomials

30th International Colloquium on Group Theoretical Methods in Physics

Celeghini, Enrico^1,2 ; Del Olmo, Mariano A.^2 ; Velasco, Miguel A.^3

Dipartimento di Fisica, Universita di Firenze, INFN-Sezione di Firenze, Sesto Fiorentino, Firenze

I50019, Italy^1

Departamento de Fisica Teorica, IMUVA, Universidad de Valladolid, Valladolid

E-47011, Spain^2

CIEMAT, Madrid, Spain^3

关键词: Formal properties;    Jacobi polynomials;    Special functions;    Symmetry groups;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/597/1/012023/pdf
DOI  :  10.1088/1742-6596/597/1/012023

来源: IOP

【 摘 要 】

We present an attempt of classification of special functions in terms of a set of formal properties mainly based on their "ladder symmetry" algebras. Thus, the "algebraic special functions" are defined. We discuss, here, the case related with the Jacobi polynomials. We construct the relevant objets associated with the corresponding symmetry group SU(2, 2): generators, subgroups, invariants and representations. Harmonic analyses based on significant subgroups for the Jacobi functions are developed.