Abstract
We present a complete classification and the construction of Mp(2n+2, R)-equivariant differential operators acting on the principal series representations, associated with the contact projective geometry on RP2n+1 and induced from the irreducible Mp(2n, R)-submodules of the Segal-Shale-Weil representation twisted by a one-parameter family of characters. The proof is based on the classification of homomorphisms of generalized Verma modules for the Segal-Shale-Weil representation twisted by a one-parameter family of characters, together with a generalization of the well-known duality between homomorphisms of generalized Verma modules and equivariant differential operators in the category of inducing smooth admissible modules.
Published by AIP Publishing.