Theta liftings on double covers of orthogonal groups
Lei, Yusheng. “Theta liftings on double covers of orthogonal groups”, Boston College, 2021. http://hdl.handle.net/2345/bc-ir:109301.
We study the generalized theta lifting between the double covers of split special orthogonal groups, which uses the non-minimal theta representations constructed by Bump, Friedberg and Ginzburg. We focus on the theta liftings of non-generic representations and make a conjecture that gives an upper bound of the first non-zero occurrence of the liftings, depending only on the unipotent orbit. We prove both global and local results that support the conjecture.