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.