Oddness of limits of automorphic Galois representations

Abstract: For classical modular forms f one knows that the associated Galois representation $\rho_f:G_{\mathbf{Q}} \to {\rm GL}_2(\overline{\mathbf{Q}}_p)$ is odd, in the sense that ${\rm det}(\rho(c))=-1$ for any complex conjugation $c$.

There is a similar parity notion for n-dimensional Galois representations which are essentially conjugate self-dual. In joint work with Ariel Weiss (Hebrew University) we prove that the Galois representations associated to certain irregular automorphic representations of U(a,b) are odd, generalizing a result of Bellaiche-Chenevier in the regular case.

I will explain our result and discuss its proof, which uses V. Lafforgue's notion of pseudocharacters and invariant theory.

algebraic geometryalgebraic topologygroup theorynumber theoryrepresentation theory

Audience: researchers in the topic

Queen Mary University of London Algebra and Number Theory Seminar