Decomposition of the spinor bundle of a quaternionic Kähler spin-manifold under the action of the fundamental 4-form (Q1842248)

The authors give the spectral decomposition of the spin bundle under the action of the fundamental 4-form \(\Omega\) on a spin quaternionic Kähler manifold \(M^{4m}\). The eigenvalues of \(\Omega\) are computed. The proof results of the study of the decomposition of the spin representation into irreducible components under the action of the group \(\text{Sp}(1) \times \text{Sp}(m)\).