Matrix Valued Spherical Functions Associated to the Complex Projective Plane

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dc.creatorGrunbaum, F. A.
dc.creatorPacharoni, I.
dc.creatorTirao, J.
dc.date2001-08-06
dc.date2001-08-28
dc.date.accessioned2026-07-07T04:42:53Z
dc.date.available2026-07-07T04:42:53Z
dc.descriptionThe main purpose of this paper is to compute all irreducible spherical functions on $G=\SU(3)$ of arbitrary type $δ\in \hat K$, where $K={\mathrm{S}}(\mathrm{U}(2)\times\mathrm{U}(1))\simeq\mathrm{U}(2)$. This is accomplished by associating to a spherical function $Φ$ on $G$ a matrix valued function $H$ on the complex projective plane $P_2(\mathbb{C})=G/K$. It is well known that there is a fruitful connection between the hypergeometric function of Euler and Gauss and the spherical functions of trivial type associated to a rank one symmetric pair $(G,K)$. But the relation of spherical functions of types of dimension bigger than one with classical analysis, has not been worked out even in the case of an example of a rank one pair. The entries of $H$ are solutions of two systems of ordinary differential equations. There is no ready made approach to such a pair of systems, or even to a single system of this kind. In our case the situation is very favorable and the solution to this pair of systems can be exhibited explicitely in terms of a special class of generalized hypergeometric functions ${}_{p+1}F_p$.
dc.description70 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0108042
dc.identifierhttp://arxiv.org/abs/math/0108042
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61979
dc.subjectRepresentation Theory
dc.subjectClassical Analysis and ODEs
dc.subject22E30; 22E46; 33C45
dc.titleMatrix Valued Spherical Functions Associated to the Complex Projective Plane
dc.typetext

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