The Residual Spectrum of F₄ Arising from Degenerate Eisenstein Series

2022/05/12 by Hezi Halawi, Halawi, Hezi
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2205.06219

openalex publication_date 2022/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a split group of type F₄ defined over a number field. We study the square-integrable automorphic representations of G that can be realized as leading terms of degenerate Eisenstein series associated to various maximal parabolic subgroups. These representations appear in the residual spectrum. The local representation theory over finite places plays a central role in our work.

Related

• Poles, Residues and Siegel-Weil Identities of Degenerate Eisenstein Series on Split Exceptional Groups of Type E_n
• Poles of degenerate Eisenstein series and Siegel-Weil identities for exceptional split groups
• The Residual Spectrum of Mp₄(A_k)
• Degenerate Eisenstein Series for Sp₄
• On the unramified Eisenstein spectrum