# Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory

F. Alberto Grünbaum^{[1]}; Inés Pacharoni; Juan Alfredo Tirao

- [1] University of California, department of mathematics, Berkeley CA 94705 (USA), Universidad Nacional de Córdoba, CIEM-FaMAF, Córdoba 5000 (Argentine)

Annales de l’institut Fourier (2005)

- Volume: 55, Issue: 6, page 2051-2068
- ISSN: 0373-0956

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topGrünbaum, F. Alberto, Pacharoni, Inés, and Alfredo Tirao, Juan. "Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory." Annales de l’institut Fourier 55.6 (2005): 2051-2068. <http://eudml.org/doc/116243>.

@article{Grünbaum2005,

abstract = {The main purpose of this paper is to present new families of Jacobi type matrix valued
orthogonal polynomials obtained from the underlying group $SU(n)$ and its
representations. These polynomials are eigenfunctions of some symmetric second order
hypergeometric differential operator with matrix coefficients. The final result holds for
arbitrary values of the parameters $\alpha ,\beta >-1$, but it is derived only for
those values that come from the group theoretical setup.},

affiliation = {University of California, department of mathematics, Berkeley CA 94705 (USA), Universidad Nacional de Córdoba, CIEM-FaMAF, Córdoba 5000 (Argentine)},

author = {Grünbaum, F. Alberto, Pacharoni, Inés, Alfredo Tirao, Juan},

journal = {Annales de l’institut Fourier},

keywords = {Matrix valued orthogonal polynomials; Jacobi polynomials; matrix valued orthogonal polynomials; symmetric spaces},

language = {eng},

number = {6},

pages = {2051-2068},

publisher = {Association des Annales de l'Institut Fourier},

title = {Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory},

url = {http://eudml.org/doc/116243},

volume = {55},

year = {2005},

}

TY - JOUR

AU - Grünbaum, F. Alberto

AU - Pacharoni, Inés

AU - Alfredo Tirao, Juan

TI - Matrix valued orthogonal polynomials of Jacobi type: the role of group representation theory

JO - Annales de l’institut Fourier

PY - 2005

PB - Association des Annales de l'Institut Fourier

VL - 55

IS - 6

SP - 2051

EP - 2068

AB - The main purpose of this paper is to present new families of Jacobi type matrix valued
orthogonal polynomials obtained from the underlying group $SU(n)$ and its
representations. These polynomials are eigenfunctions of some symmetric second order
hypergeometric differential operator with matrix coefficients. The final result holds for
arbitrary values of the parameters $\alpha ,\beta >-1$, but it is derived only for
those values that come from the group theoretical setup.

LA - eng

KW - Matrix valued orthogonal polynomials; Jacobi polynomials; matrix valued orthogonal polynomials; symmetric spaces

UR - http://eudml.org/doc/116243

ER -

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