Spherical harmonic analysis on affine buildings

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dc.creatorParkinson, James
dc.date2006-04-04
dc.date.accessioned2026-07-07T07:10:28Z
dc.date.available2026-07-07T07:10:28Z
dc.descriptionTo each regular affine building there is naturally associated a commutative algebra A spanned by vertex set averaging operators. In this paper we study the algebra homomorphisms from A into the complex numbers. In particular, we provide two explicit formulae for these homomorphisms; one in terms of the Macdonald spherical functions, and another as an integral over the boundary of the building. We also determine the associated Plancherel measure, and we compute the l^2-operator norms of each basis element of A.
dc.descriptionTo appear in Mathematische Zeitschrift
dc.identifierhttps://arxiv.org/abs/math/0604058
dc.identifierhttp://arxiv.org/abs/math/0604058
dc.identifierdoi:10.1007/s00209-005-0924-4
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111434
dc.subjectFunctional Analysis
dc.subject20E42; 43A90
dc.titleSpherical harmonic analysis on affine buildings
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