Siegel-Weil type identities for general linear groups related to parabolic induction from two Speh representations

Abstract

We prove identities of Siegel-Weil type for Eisenstein series on general linear groups, attached to parabolic induction from two Speh representations corresponding to the same irreducible, cuspidal representation. Such an identity relates a residue, at a (simple) pole of an Eisenstein series, as above, to a value of a similarly structured Eisenstein series at a point of holomorphy.