Local theta correspondence and nilpotent invariants

TL;DR

This paper surveys recent findings on how nilpotent invariants like generalized Whittaker models and associated characters behave under local theta correspondence, emphasizing the significance of a specific double fiberation of moment maps.

Contribution

It provides a comprehensive overview of recent results on the interaction between nilpotent invariants and local theta correspondence, highlighting the role of moment maps.

Findings

Nilpotent invariants are studied under local theta correspondence.

The behavior of generalized Whittaker models and associated characters is analyzed.

A special double fiberation of moment maps is identified as significant.

Abstract

We consider two types of nilpotent invariants associated to smooth representations, namely generalized Whittaker models, and associated characters (in the case of a real reductive group). We survey some recent results on the behavior of these nilpotent invariants under local theta correspondence, and highlight the special role of a certain double fiberation of moment maps.