​Seminar: l-modular theta correspondence

Seminar| Institute of Mathematical Sciences

Time:Wednesday, September 10th, 2025,13:00-14:00

Abstract: 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.