Symplectic Dirac Operator and its Higher Spin Analogues

Abstract

Symplectic Dirac operator is a symplectic counterpart of the classical Dirac operator known from Clifford analysis or Riemannian geometry. We introduce this operator and mention some of its representation theoretical aspects, like the Howe type duality. As a consequence of this duality, we display a theorem relating the spectra of the symplectic Dirac operator and the symplectic Rarita‐Schwinger operator.