Infinite Dimensional Multiplicity Free Spaces I: Limits of Compact Commutative Spaces

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dc.creatorWolf, Joseph A.
dc.date2008-01-25
dc.date.accessioned2026-07-07T08:56:26Z
dc.date.available2026-07-07T08:56:26Z
dc.descriptionWe study direct limits $(G,K) = \varinjlim (G_n,K_n)$ of compact Gelfand pairs. First, we develop a criterion for a direct limit representation to be a multiplicity--free discrete direct sum of irreducible representations. Then we look at direct limits $G/K = \varinjlim G_n/K_n$ of compact riemannian symmetric spaces, where we combine our criterion with the Cartan--Helgason Theorem to show in general that the regular representation of $G = \varinjlim G_n$ on a certain function space $\varinjlim L^2(G_n/K_n)$ is multiplicity free. That method is not applicable for direct limits of nonsymmetric Gelfand pairs, so we introduce two other methods. The first, based on ``parabolic direct limits'' and ``defining representations'', extends the method used in the symmetric space case. The second uses some (new) branching rules from finite dimensional representation theory. In both cases we define function spaces $\cA(G/K)$, $\cC(G/K)$ and $L^2(G/K)$ to which our multiplicity--free criterion applies.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/0801.3869
dc.identifierhttp://arxiv.org/abs/0801.3869
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146610
dc.subjectRepresentation Theory
dc.subjectDifferential Geometry
dc.subject22E45; 22E65; 22E25; 22G05; 43A85; 43A90; 53C35
dc.titleInfinite Dimensional Multiplicity Free Spaces I: Limits of Compact Commutative Spaces
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