2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60236We give a method of decomposing bundle-valued polynomials compatible with the action of the Lie group $Spin(n)$, where important tools are $Spin(n)$-equivariant operators and their spectral decompositions. In particular, the top irreducible component is realized as an intersection of kernels of these operators.11 pages, LaTeX2eDifferential GeometryRepresentation TheorySpectral Theorytext