Zelevinsky Duality on Basic Local Shimura Varieties

Abstract

We give a simple proof of a general result describing the action of the Zelevinsky involution on the cohomology of certain basic local Shimura varieties, using the machinery of Fargues-Scholze. As an application, we generalize earlier results of Fargues and Mieda on the action of the Zelevinsky involution on the cohomology of $G{L}_n$ and $GS{p}_4$ type basic local Shimura varieties, respectively.

Comments and corrections are welcome! v2 fixed some small mistakes