Spherical functions of fundamental K-types associated with the n-dimensional sphere
Abstract
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.
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Tirao, J. A. y Zurrián, I. N. (2014). Spherical functions of fundamental K-types associated with the n-dimensional sphere. Symmetry, Integrability and Geometry, 10, 1-41. https://doi.org/10.3842/SIGMA.2014.071