Spectra of the Laplacian on the Cayley projective plane (Q1375756)

Let \(\text{Ca}P^2 = F_4/\text{Spin}(9)\) denote the Cayley projective plane. The goal of the paper under review is to find the decomposition of the vector space of smooth \(p\)-forms on \(\text{Ca}P^2\) into the direct sum of irreducible \(F_4\)-submodules and to find the corresponding eigenvalues of the Laplacian. This problem is completely solved for \(0\leq p\leq 5\), using Frobenius reciprocity and the results of J. Lepovsky about the branching law of the pair \((F_4, \text{Spin}(9))\).