Poles of Eisenstein series on general linear groups induced from two Speh representations

2024/10/30 by Ginzburg, David, Soudry, David
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2410.23026

Abstract

We determine the poles of the Eisenstein series on a general linear group, induced from two Speh representations, Δ(τ,m₁)|⋅|^s×Δ(τ,m₂)|⋅|^-s, Re(s)≥ 0, where τ is an irreducible, unitary, cuspidal, automorphic representation of GL_n(\bf A). The poles are simple and occur at s=(m₁+m₂)/(4)-(i)/(2), 0≤ i≤ min(m₁,m₂)-1. Our methods also show that when m₁=m₂, the above Eisenstein series vanish at s=0.

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