The differential form spectrum of quaternionic hyperbolic spaces

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.