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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.

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18. Februar 2020, 15:15-16:15

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S2|15 401

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AG Algebra

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