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Artículo

Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II

Koelink, Erik; Van Pruijssen, Maarten; Román, Pablo ManuelIcon
Fecha de publicación: 04/2013
Editorial: Kyoto Univ
Revista: Publications Of The Research Institute For Mathematical Sciences
ISSN: 0034-5318
Idioma: Inglés
Tipo de recurso: Artículo publicado
Clasificación temática:
Matemática Pura

Resumen

In a previous paper we have introduced matrixvalued analogues of the Chebyshev polynomials by studying matrix-valued spherical functions on SU(2) × SU(2). In particular the matrix-size of the polynomials is arbitrarily large. In this paper, the matrix-valued orthogonal polynomials and the corresponding weight function are studied. In particular, we calculate the LDU-decomposition of the weight where the matrix entries of L are given in terms of Gegenbauer polynomials. The monic matrix-valued orthogonal polynomials P_n are expressed in terms of Tirao's matrix-valued hypergeometric function using the matrix-valued differential operators of first and second order of which the P_n's are eigenfunctions. From this result we obtain an explicit formula for coefficients in the three-term recurrence relation satisfied by the polynomials Pn. These differential operators are also crucial in expressing the matrix entries of P_nL as a product of a Racah and a Gegenbauer polynomial. We also present a group-theoretic derivation of the matrix-valued differential operators by considering the Casimir operators corresponding to SU(2) × SU(2).
Palabras clave: Spherical Functions , Matrix Valued Orthogonal Polynomials
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info:eu-repo/semantics/openAccess Excepto donde se diga explícitamente, este item se publica bajo la siguiente descripción: Creative Commons Attribution-NonCommercial-ShareAlike 2.5 Unported (CC BY-NC-SA 2.5)
Identificadores
URI: http://hdl.handle.net/11336/12273
DOI: http://dx.doi.org/10.4171/PRIMS/106
URL: http://www.ems-ph.org/journals/show_abstract.php?issn=0034-5318&vol=49&iss=2&ran
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Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Koelink, Erik; Van Pruijssen, Maarten; Román, Pablo Manuel; Matrix-valued Orthogonal Polynomials Related to (SU(2) × SU(2), SU(2)), II; Kyoto Univ; Publications Of The Research Institute For Mathematical Sciences; 49; 2; 4-2013; 271-312
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