Howe and Tan investigated a degenerate principal series representation of indefinite orthogonal groups and completely described its composition series. Their work implies the existence of a unique unitarizable irreducible submodule, which is isomorphic to a non-tempered derived functor module. Our research focuses on the theta liftings locally corresponding to this representation.
In this talk, we will introduce the Fourier expansion of the theta liftings and the idea of their calculations. Moreover, we will talk about future work in the higher degree case.
A part of this talk is based on the joint work with Takuya Miyazaki.