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.

中文翻译：

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正交组上较高的模块化形式的回调

我们将微分算子应用于正交群O⁢（2，ℓ）{\ mathrm {O}（2，\ ell）}上的模块化形式，以构造特殊循环上的无限系列的模块化形式。这些算子将拟回拉广义化。θ提升的子空间得以保留；特别是，（晶格指数）Jacobi形式the的升力较高的回撤是部分发展系数the的θ升力。对于（2,2）{（2,2）}和（2,3）{（2,3）}的某些特征格，对于它们的解释为Hilbert–Siegel模块化形式，我们观察到较高的回撤同时发生由Cohen和Ibukiyama引入的差分运算符。