2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95096We study geometric first order differential operators on quaternionic Kähler manifolds. Their principal symbols are related to the enveloping algebra and Casimir elements for $\Sp(1)\Sp(n)$. This observation leads to anti-symmetry of the principal symbols and Bochner-Weitzenböck formulas for operators. As an application, we estimate the first eigenvalues of them.32page. minor revision including new observationsDifferential Geometrytext