The $p$-adic Howe Correspondence and Affine Hecke Algebras
Time: 2024-07-12
Published By: He Liu
Speaker(s): Anne-Marie Aubert(Sorbonne Université)
Time: 14:00-15:00 July 17, 2024
Venue: Room 78301, Jingchunyuan 78, BICMR
We will consider $p$-adic reductive dual pairs $(G,G')$, where $G$ is symplectic and $G'$ orthogonal, and explain how the compatibility of the Howe correspondence with parabolic induction leads to a collection of correspondences between simple modules of affine Hecke algebras $\mathcal{H}(G,\mathfrak{s})$ and $\mathcal{H}(G',\mathfrak{s}')$, where $\mathfrak{s}'$ is explicitely described in term of $\mathfrak{s}$.
Next, we will translate these correspondences on the Galois side of the local Langlands correspondence in terms of enhanced $L$-parameters.
In the case of tempered representations, we will be able to derive correspondences at the level of $C^*$-algebras, whenever $G$ and $G'$ have almost equal rank.
