The $p$-adic Howe Correspondence and Affine Hecke Algebras -

The $p$ -adic Howe Correspondence and Affine Hecke Algebras

发布时间：2024年07月12日浏览次数：1170 发布者: He Liu

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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

H (G, s)

and

H (G^{'}, s^{'})

, where

s^{'}

is explicitely described in term of

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.

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The p-adic Howe Correspondence and Affine Hecke Algebras

The $p$ -adic Howe Correspondence and Affine Hecke Algebras