The $p$-adic Howe Correspondence and Affine Hecke Algebras
发布时间：2024年07月12日
浏览次数：577
发布者: He Liu
主讲人： Anne-Marie Aubert(Sorbonne Université)
活动时间： 从 2024-07-17 14:00 到 15:00
场地： 北京国际数学研究中心，镜春园78号院（怀新园）78301室
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.
