Higher pullbacks of modular forms on orthogonal groups

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 $\varphi$ are theta lifts of partial development coefficients of $\varphi$. 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.

20 pages

References in corpus (1)

• The Kodaira dimension of the moduli of K3 surfaces

Cited by in corpus (1)

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