2015/12/27 by Křižka, Libor, Somberg, Petr
#53C30 #53D05 #81R25 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1512.08203
We present a complete classification and the construction of Mp(2n+2,ℝ)-equivariant differential operators acting on the principal series representations, associated to the contact projective geometry on \mathbbRP2n+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.