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Geometric interplay between function subspaces and their rings of differential operators
Department of Mathematics, Stockholm University, Stockholm, Sweden.
University of Gävle, Department of Mathematics, Natural and Computer Sciences, Ämnesavdelningen för matematik och statistik. (Matematik)
2006 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 359, no 5, 2075-2108 p.Article in journal (Refereed) Published
Abstract [en]

We study, in the setting of algebraic varieties, finite-dimensional spaces of functions $V$ that are invariant under a ring $\Dc^V$ of differential operators, and give conditions under which $\Dc^V$ acts irreducibly. We show how this problem, originally formulated in physics \cite{kamran-Milson-Olver:invariant,turbiner:bochner}, is related to the study of principal parts bundles and Weierstrass points \cite{EGA4,laksov-thorup}, including a detailed study of Taylor expansions. Under some conditions it is possible to obtain $V$ and $\Dc^V$ as global sections of a line bundle and its ring of differential operators. We show that several of the published examples of $\Dc^V$ are of this type, and that there are many more - in particular, arising from toric varieties.

Place, publisher, year, edition, pages
2006. Vol. 359, no 5, 2075-2108 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:hig:diva-2449ISI: 000243610400007Scopus ID: 2-s2.0-77950984285OAI: oai:DiVA.org:hig-2449DiVA: diva2:119111
Available from: 2007-04-29 Created: 2007-04-29 Last updated: 2016-10-30Bibliographically approved

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