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Geometric interplay between function subspaces and their rings of differential operators

Rikard Bögvad·Rolf Källström
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Abstract

We study, in the setting of algebraic varieties, finite-dimensional spaces of functions V that are invariant under a ring D^V of differential operators, and give conditions under which D^V acts irreducibly. We show how this problem, originally formulated in physics (Kamran-Milson-Olver), is related to the study of principal parts bundles and Weierstrass points (Laksov-Thorup), including a detailed study of Taylor expansions. Under some conditions it is possible to obtain V and D^V as global sections of a line bundle and its ring of differential operators. We show that several of the published examples of D^V are of this type, and that there are many more -- in particular arising from toric varieties.

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Rikard Bögvad, Rolf Källström. 2004-03-24. Geometric interplay between function subspaces and their rings of differential operators. https://arxiv.org/abs/math/0403409

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