A characterization of the L²-range of the Poisson transforms on a class of vector bundles over the quaternionic hyperbolic spaces

2023/01/12 by Boussejra, Abdelhamid, Chaib, Achraf Ouald
#43A85-43A90 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2301.05304

Abstract

We study the L²-boundedness of the Poisson transforms associated to the homogeneous vector bundles Sp(n,1)×_{Sp(n)× Sp(1)} V_τ over the quaternionic hyperbolic spaces Sp(n,1)/Sp(n)× Sp(1) associated with irreducible representations τ of Sp(n)× Sp(1) which are trivial on Sp(n). As a consequence, we describe the image of the section space L²(Sp(n,1)×_{Sp(n)× Sp(1)} V_τ) under the generalized spectral projections associated to a family of eigensections of the Casimir operator.

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