The Meromorphic continuation of the resolvent of the Laplacian on line bundles over ℂH(n)

Will, Cynthia E.

doi:10.2140/pjm.2003.209.157

Cited by 5 publications

(2 citation statements)

References 8 publications

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“…Complete results for most of the rank-two cases were proved in a series of papers by Hilgert, Pasquale and Przebinda [HPP16,HPP17b,HPP17a]. For the Laplacian acting on line bundles over complex hyperbolic spaces, the resonances has been completely determined by Will in [Wil03]. The complete list of the resonances for the Laplacian acting on sections on E τ , when G/K if of rank one and τ is arbitrary was determined in [Rob22].…”

Section: Introductionmentioning

confidence: 99%

“…These representations have been determined for the scalar rank-one case by different method in [MW00] and in [HP09]. Moreover, in [Wil03], this has been also done for the case of SL(2, Ê), in the (line) bundle case. For the general rank one case, the residue representations were determined in [Rob22] under the assumption that the resonances arise from the poles the trivial Plancherel density, which implies that τ has to occur in the spherical principal series representations.…”

Section: Introductionmentioning

confidence: 99%

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Residue representations -- the rank one case

Roby¹

2022

Preprint

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With each resonance of the Laplacian acting on the compactly supported sections of a homogeneous vector bundle over a Riemannian symmetric space of the non-compact type, One can associate a residue representation. The purpose of this paper is to study them. The symmetric space is assumed to have rank-one but the irreducible representation τ of K defining the vector bundle is arbitrary. We give an algorithm that aims at determining if these representations are irreducible, finding their Langlands parameters, their Gelfand-Kirillov dimensions and wave front sets. As an example, we apply this algorithm to the Laplacian of the p-forms in the cases of all the classical real rank-one Lie groups.

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