Artículo
Matrix-valued orthogonal polynomials related to (SU(2)×SU(2), diag)
Fecha de publicación:
01/2012
Editorial:
Oxford University Press
Revista:
International Mathematics Research Notices
ISSN:
1073-7928
e-ISSN:
1687-0247
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
The matrix-valued spherical functions for the pair (K×K,K), K=SU(2), are studied. By restriction to the subgroup A, the matrix-valued spherical functions are diagonal. For suitable set of spherical functions, we take these diagonals as a matrix-valued function, which are the full spherical functions. Their orthogonality is a consequence of the Schur orthogonality relations. From the full spherical functions, we obtain matrix-valued orthogonal polynomials of arbitrary size, and they satisfy a three-term recurrence relation which follows by considering tensor product decompositions. An explicit expression for the weight and the complete block-diagonalization of the matrix-valued orthogonal polynomials is obtained. From the explicit expression, we obtain right-hand-sided differential operators of first and second order for which the matrix-valued orthogonal polynomials are eigenfunctions. We study the low-dimensional cases explicitly, and for these cases additional results, such as the Rodrigues' formula and being eigenfunctions to first-order differential-difference and second-order differential operators, are obtained. © 2012 The Author(s).
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Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
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), diag); Oxford University Press; International Mathematics Research Notices; 2012; 24; 1-2012; 5673-5730
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