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.
A conjecture of Kudla and Rallis on quotients of degenerate principal series
10.10.2023 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: