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Classification of irreducible representations of metaplectic covers of the general linear group over a non-archimedean local field

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arxiv 2206.14731 v1 pith:4YDNF7DO submitted 2022-06-29 math.RT math.NT

Eyal Kaplan , Erez Lapid , Jiandi Zou This is my paper · ORCID
classification math.RTmath.NT
keywords classificationrepresentationsfieldirreduciblelocalmetaplecticnon-archimedeananalogous
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abstract

Let $F$ be a non-archimedean local field. The classification of the irreducible representations of $GL_n(F)$, $n\ge0$ in terms of supercuspidal representations is one of the highlights of the Bernstein--Zelevinsky theory. We give an analogous classification for metaplectic coverings of $GL_n(F)$, $n\ge0$.

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Cited by 1 Pith paper

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  1. The spectrum of the symplectic Grassmannian and $\mathrm{Mat}_{n,m}$

    math.RT 2025-06 conditional novelty 7.0 of 10

    The paper determines the spectrum of Schwartz functions on Mat_{n,m} and the symplectic Grassmannian using rho-derivatives and the Local Structure Theorem, yielding new proofs and explicit local lifts.

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