Vol. 16, No. 5, 2022

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Entirety of certain cuspidal Eisenstein series on Kac–Moody groups

Lisa Carbone, Kyu-Hwan Lee and Dongwen Liu

Vol. 16 (2022), No. 5, 1099–1119
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 the cuspidal Eisenstein series are entire on the full complex plane.

Keywords
Eisenstein series, Kac–Moody groups, entirety
Mathematical Subject Classification
Primary: 11F70, 20G44
Milestones
Received: 26 August 2020
Revised: 8 May 2021
Accepted: 25 August 2021
Published: 16 August 2022
Authors
Lisa Carbone
Department of Mathematics
Rutgers
The State University of New Jersey
Piscataway, NJ
United States
Kyu-Hwan Lee
Department of Mathematics
University of Connecticut
Storrs, CT
United States
Dongwen Liu
School of Mathematical Sciences
Zhejiang University
Hangzhou
China