Symplectic Dirac cohomology and lifting of characters to metaplectic groups

Abstract: We formulate the transfer factor of character lifting from orthogonal groups to symplectic groups by Adams in the framework of symplectic Dirac cohomology for the Lie superalgebras and the Rittenberg-Scheunert correspondence of representations of the Lie superalgebra $\fro\frsp(1|2n)$ and the Lie algebra $\fro(2n+1)$. This leads to formulation of a direct lifting of characters from the linear symplectic group $Sp(2n,\bbR)$ to its nonlinear covering metaplectic group $Mp(2n,\bbR)$.