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Spectre de l’opérateur de Dirac sur les espaces projectifs quaternioniens. (Spectrum of the Dirac operator on quaternionic projective spaces). (French) Zbl 0753.47039

The eigenvalues of the Dirac operator on quaternionic projective spaces \(HP^ n\) are explicitly obtained in this note in terms of the Casimir coefficients corresponding to some irreducible representations of the complex symplectic group \(G\). The main auxiliary result is a decomposition lemma concerning the representation of \(H\) on the spinor space.

MSC:

47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
22A25 Representations of general topological groups and semigroups
47S10 Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory
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