Howe's theory of reductive dual pairs is one of the most useful tools for understanding representations of classical groups. In this series of talks we will explore the compatibility between Howe's Theta-lifting correspondence and some of the nilpotent invariants associated to a representation of a reductive group G. (Like wave front set, generalized Whittaker models, associated cycle...)

In the first talk, I will review the classification of nilpotent orbits for a classical group and introduce the nilpotent invariants of interest. Then I will discuss a generalization of a result of Moeglin regarding the compatibility of Howe's Theta-lifting correspondence and the space of generalized Whittaker models.

In the second talk I will describe further improvements to this result involving invariant linear functionals and look at some applications.