Representation Theory and Noncommutative Geometry, Paris

Modular local theta correspondence

10 mars 2025, 17:00

1h

Amphitheater Darboux (IHP)

Orateur

Justin Trias (University of East Anglia)

Description

The local theta correspondence over a non-Archimedean local field of residual characteristic p asserts a bijection between (subsets of) irreducible complex representations of two reductive groups forming a dual pair in a symplectic group.
In this talk, I will explain how this theory can be generalized to $l$-modular representations — i.e. when the coefficient field has positive characteristic $l$, distinct from $p$. Provided that l is sufficiently large relative to the size of the dual pair, this generalisation also results in a bijection, which we refer to as the $l$-modular theta correspondence. However, for certain values of~$l$, such a bijection fails to hold.