I happened upon this paper, can any of you people come up with a
practical application for it?
Abstract. By using harmonic analysis and representation theory, we
determine explicitly
the L2 spectrum of the Hodge-de Rham Laplacian acting on quaternionic
hyperbolic
spaces and we show that the unique possible discrete eigenvalue and the
lowest
continuous eigenvalue can both be realized by some subspace of
hypereffective differential
forms. Similar results are obtained also for the Bochner Laplacian.
http://emmanuel.pedon.free.fr/maths/prepublis/SpectreQuat.pdf
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