On unipotent representations of ramified 𝑝-adic groups

Solleveld, Maarten

doi:10.1090/ert/652

On unipotent representations of ramified $p$-adic groups
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by Maarten Solleveld;

Represent. Theory 27 (2023), 669-716

DOI: https://doi.org/10.1090/ert/652

Published electronically: July 26, 2023

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Abstract:

Let $G$ be any connected reductive group over a non-archimedean local field. We analyse the unipotent representations of $G$, in particular in the cases where $G$ is ramified. We establish a local Langlands correspondence for this class of representations, and we show that it satisfies all the desiderata of Borel as well as the conjecture of Hiraga, Ichino and Ikeda about formal degrees.

This generalizes work of Lusztig and of Feng, Opdam and the author, to reductive groups that do not necessarily split over an unramified extension of the ground field.

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Representation Theory

On unipotent representations of ramified $p$-adic groups
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Abstract: