Theta liftings on higher covers of symplectic groups

Abstract

We study a new lifting of automorphic representations using the theta representation ϴ on the 4-fold cover of the symplectic group, $\overline{\Sp}_{2r}(\A)$. This lifting produces the first examples of CAP representations on higher degree metaplectic covering groups. Central to our analysis is the identification of the maximal nilpotent orbit associated to ϴ. We conjecture a natural extension of Arthur's parameterization of the discrete spectrum to $\overline{\Sp}_{2r}(\A)$. Assuming this, we compute the effect of our lift on Arthur parameters and show that the parameter of a representation in the image of the lift is non-tempered. We conclude by relating the lifting to the dimension equation of Ginzburg to predict the first non-trivial lift of a generic cuspidal representation of $\overline{\Sp}_{2r}(\A)$.