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 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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| Main Authors: | , |
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| Format: | article biblioteca |
| Language: | eng |
| Published: |
2014
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| Subjects: | Matrix-valued spherical functions, Matrix orthogonal polynomials, The matrix hypergeometric operator, n-dimensional sphere, |
| Online Access: | http://hdl.handle.net/11086/20304 https://doi.org/10.3842/SIGMA.2014.071 |
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