Abstract
We apply differential operators to modular forms on orthogonal groups
O
(
2
,
ℓ
)
{\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 ϕ are theta lifts of partial development coefficients of ϕ. For certain lattices of signature
(
2
,
2
)
{(2,2)}
and
(
2
,
3
)
{(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.
Higher pullbacks of modular forms on orthogonal groups
