Jacquet modules of tempered representations of O(2n).
ABSTRACT
The highest derivatives in the sense of Jantzen and Minguez are partial information of Jacquet modules, which are almost enough to determine irreducible representations. In this talk, we describe the highest derivatives of irreducible tempered representations of quasi-split even full orthogonal groups. In the proof, we extend Xu's argument directly. We will explain an issue appearing in this extension, and how to solve it. This is a part of joint project of a team including Alberto Minguez.