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Differential operators, holomorphic projection, and singular forms. (English) Zbl 0829.11029

As mentioned in the title, the author applies his theory of differential operators on Hermitian symmetric spaces to (1) the holomorphic projection and (2) singular forms.
As for (1), the author generalizes the holomorphic projection to the case of an arbitrary classical group acting on a Hermitian symmetric space of noncompact type, which approaches, in future, the problem of the algebraicity of the critical values of certain zeta-functions for that case. As for (2), a generalization of “When is the Siegel modular form singular” to forms of the classical domains (of non-compact type) is investigated.
The main idea behind both (1), (2) are certain relations between inner products under the influence of differential operators.
Reviewer: K.Katayama (Tokyo)

MSC:

11F60 Hecke-Petersson operators, differential operators (several variables)
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
32N15 Automorphic functions in symmetric domains
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