A regularized theta lift on the symmetric space of $SL_N$

Abstract

We define a regularized lift from harmonic weak Maass forms of weight $2-N$ to differential forms of degree $N-1$ on the symmetric space $\SL_N(\R)/\SO(N)$, that are smooth outside of certain modular symbols. We show that this lift is adjoint to the derivative of a theta lift. We compute periods of the regularized lift over tori and relate them to Fourier coefficients of Hilbert-Eisenstein series.