Entirety of certain cuspidal Eisenstein series on Kac--Moody groups

2020/08/26 by Lisa Carbone, Carbone, Lisa, Kyu‐Hwan Lee +4
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.2008.11559

openalex publication_date 2020/08/26 · arxiv created 2021/05/08 · arxiv updated 2021/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be an infinite-dimensional representation-theoretic Kac--Moody group associated to a nonsingular symmetrizable generalized Cartan matrix. We consider Eisenstein series on G induced from unramified cusp forms on finite-dimensional Levi subgroups of maximal parabolic subgroups. Under a natural condition on maximal parabolic subgroups, we prove that the cuspidal Eisenstein series are entire on the full complex plane.

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