On the lattice model of the Weil representation

2024/04/05 by Chunhui Wang, Wang, Chun-Hui
Chemistry · Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2404.03983

openalex publication_date 2024/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a local field. In the case of F being the real field, Pierre Cartier constructed Heisenberg-Weil representations of a Heisenberg group in families using non-self-dual lattices. This result was later reformulated by Jae-Hyun Yang in another paper. We extend this family of representations to a representation of a Jacobi subgroup by incorporating a rational Metaplectic group. In the case of F being a non-archimedean local field of odd residual characteristic or a finite unramified extension of the field of 2-adic numbers, we obtain similar results for a Jacobi group by incorporating a Metaplectic group.

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• Correspondance thêta locale ℓ-modulaire I : groupe métaplectique, représentation de Weil et Θ-lift
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• Realizing the local Weil representation over a number field
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