New types of Siegel-Weil formulas

David Soudry (Tel Aviv U)

Apr 13. 2022, 14:30 — 15:15

I will present several conjectural identities which bear a striking similarity with the Kudla-Rallis regularized Siegel-Weil formula. The key players, in the role of theta series, are the residues of Eisenstein series on symplectic groups, induced from Speh representations on Siegel parabolic subgroups. I will focus on a special case, already highly nontrivial, of the residual Eisenstein series on Sp(4m), Theta(\tau,4m), induced from a Speh representation on GL(2m) corresponding to a cuspidal representation \tau on GL(2), with trivial central character and non-vanishing L-function at 1/2, the pole of the Eisenstein series being taken at s=m/2. I will examine a regularized "Theta lift" of Theta(\tau,4l) to Sp(4m), m>l-1, where the "Theta kernel" is Theta(\tau,4(m+l)), restricted to Sp(4l) x Sp(4m). The result is a residual Eisenstein series induced from the tensor product of the Speh representation of GL(2l) corresponding to \tau and Theta(\tau, 4(m-l)). For a good choice of data, this is equal to a special value of an Eisenstein series on Sp(4m) induced from the Speh representation of GL(2m) corresponding to \tau. This is an ongoing joint work with David Ginzburg.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Minimal Representations and Theta Correspondence (Workshop)
Wee Teck Gan (U of Singapore)
Marcela Hanzer (U Zagreb)
Alberto Minguez (U of Vienna)
Goran Muic (U Zagreb)
Martin Weissman (UC Santa Cruz)