A conjecture of Kudla and Rallis on quotients of degenerate principal series

10.10.2023 13:15 - 14:45

Johannes Droschl (U Vienna)

In this talk we prove a conjecture of Kudla and Rallis on degenerate principal series, namely that all of its irreducible quotients appear with multiplicity one. In particular, we obtain a new proof of the conservation relation of the local Theta correspondence in Type I. The main idea is to consider a filtration of the parabolic reduction of a degenerate principal series, which is induced from a suitable stratification of the underlying Lagrangian Grassmanian.

This allows us to reduce the conjecture to the Howe correspondence in Type II.  All of the presented results are work in progress.


H. Grobner, A. Minguez-Espallargas, A. Mellit


BZ 2, 2. OG., OMP 1