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

Abstract

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The main purpose of this paper is to present new families of Jacobi type matrix valued orthogonal polynomials obtained from the underlying group S U ( 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 α , β > - 1 , but it is derived only for those values that come from the group theoretical setup.

How to cite

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Grünbaum, 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 $\alpha ,\beta &gt;-1$, 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 $\alpha ,\beta &gt;-1$, 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 -

References

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