Higher pullbacks of modular forms on orthogonal groups

RWTH Publications (RWTH Aachen)

Abstract

We apply differential operators to modular forms on orthogonal groups $\mathrm{O}(2, \ell)$ to construct infinite families of modular forms on special cycles. These operators generalize the quasi-pullback. The subspaces of theta lifts are preserved; in particular, the higher pullbacks of the lift of a (lattice-index) Jacobi form $\phi$ are theta lifts of partial development coefficients of $\phi$. For certain lattices of signature (2, 2) and (2, 3), for which there are interpretations as Hilbert-Siegel modular forms, we observe that the higher pullbacks coincide with differential operators introduced by Cohen and Ibukiyama.

Authors 1

1. Brandon Williams corresponding Aachen Lehrstuhl A für Mathematik

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl A für Mathematik , RWTH Aachen University , 52056 Aachen , Germany