Poles of Eisenstein Series on General Linear Groups Induced from Two Speh Representations

Explore the poles of Eisenstein series on GL(n(m_1+m_2), A) induced from two Speh representations in this advanced mathematics lecture. Delve into the determination of poles based on irreducible cuspidal representations of GL(n,A) with specific "lengths" m_1 and m_2, featuring complex parameters (s,-s) where Re(s) is non-negative. Learn how these poles are proven to be simple and discover the methods used to determine the wave front sets of their residues. Examine the descent operation techniques analogous to Bernstein-Zelevinsky derivatives, and understand the significant finding that when m_1=m_2, the Eisenstein series vanish at s=0. This research presentation, delivered as part of the Workshop on "Eisenstein Series, Spaces of Automorphic Forms, and Applications," represents joint work with David Ginzburg and provides deep insights into the analytical properties of these important mathematical objects in the theory of automorphic forms and representation theory.