Entirety of certain cuspidal Eisenstein series on Kac–Moody groups

Carbone, Lisa; Lee, Kyu-Hwan; Liu, Dongwen

doi:10.2140/ant.2022.16.1099

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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

DOI: 10.2140/ant.2022.16.1099

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.

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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

Vol. 16, No. 5, 2022