Spherical functions of fundamental K-types associated with the n-dimensional sphere

In this paper, we describe the irreducible spherical functions of fundamental K-types associated with the pair (G, K) = (SO(n + 1), SO(n)) in terms of matrix hypergeometric functions. The output of this description is that the irreducible spherical functions of the same K-fundamental type are encode...

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Autores principales: Tirao, Juan Alfredo, Zurrián, Ignacio Nahuel
Formato: article
Lenguaje:Inglés
Publicado: 2021
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Acceso en línea:http://hdl.handle.net/11086/20304
https://doi.org/10.3842/SIGMA.2014.071
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Sumario:In this paper, we describe the irreducible spherical functions of fundamental K-types associated with the pair (G, K) = (SO(n + 1), SO(n)) in terms of matrix hypergeometric functions. The output of this description is that the irreducible spherical functions of the same K-fundamental type are encoded in new examples of classical sequences of matrix-valued orthogonal polynomials, of size 2 and 3, with respect to a matrix-weight W supported on [0, 1]. Moreover, we show that W has a second order symmetric hypergeometric operator D.