Theta liftings for $({\mathrm{GL}}_n,{\mathrm{GL}}_n)$ type dual pairs of loop groups

Abstract

In this article we prove the theta liftings of a cusp form on the loop group ${\mathrm{GL}}_n$ induced from a classical cusp form for the loop group ``dual pair'' $({\mathrm{GL}}_n,{\mathrm{GL}}_n)$ is an Eisenstein series.

arXiv comment26 pages, with more complete proofs