Some Combinatorics in the Cancellation of Poles of Eisenstein Series for $GL(n,{\mathbb{A}}_{\mathbb{Q}})$

Abstract

The cancellations of poles of degenerate Eisenstein series were studied by Hanzer and Muić. This paper generalizes the method and the result to Eisenstein series constructed from inducing two Speh representations $\Delta (\tau ,m)|\cdot {|}^{s_1}\otimes \Delta (\tau ,n)|\cdot {|}^{s_2}$ for the group $GL(m+n,{\mathbb{A}}_{\mathbb{Q}})$ for self-dual cuspidal automorphic representation $\tau$ by describing the combinatorics of the relevant Weyl group coset.