Stable blocks en enhanced Langlands parameters

Abstract: The decomposition into Bernstein blocks of the category of smooth representations of a p-adic group G admits a Galois analogue in terms of enhanced L-parameters, in which the role of supercuspidal representations is played by « cuspidal » enhanced L-parameters, a notion that originates in the construction by Lusztig of the generalized Springer correspondence.

We will formulate sufficient conditions to be satisfied by the local Langlands correspondence for the supercuspidal representations of the Levi subgroups of G in order to allow to construct a canonical bijection between the associated blocks on both sides.

Next, when these conditions are satisfied, we will explain how to gather these blocks together into bigger ones that are unions of L-packets.

algebraic geometrynumber theory

Audience: researchers in the topic

Luxembourg Number Theory Day 2024