Holonomic modules for rings of invariant differential operators
نویسندگان
چکیده
منابع مشابه
Dimension, Multiplicity, Holonomic Modules, and an Analogue of the Inequality of Bernstein for Rings of Differential Operators in Prime Characteristic
Let K be an arbitrary field of characteristic p > 0 and D(Pn) the ring of differential operators on a polynomial algebra Pn in n variables. A long anticipated analogue of the inequality of Bernstein is proved for the ring D(Pn). In fact, three different proofs are given of this inequality (two of which are essentially characteristic free): the first one is based on the concept of the filter dim...
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We study Gorenstein dimension and grade of a module M over a filtered ring whose assosiated graded ring is a commutative Noetherian ring. An equality or an inequality between these invariants of a filtered module and its associated graded module is the most valuable property for an investigation of filtered rings. We prove an inequality G-dimM ≤ G-dimgrM and an equality gradeM = grade grM , whe...
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This note announces a number of results on the structure of differential modules over differential rings, where differential ring means a ring with a family of derivations and differential module means a module having a family of operators compatible with the derivations of the ring. To fix notation, throughout the paper we let A denote an associative ring, M = AM an 4-module, k the correspondi...
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on the complex upper half-plane H, provably invariant under the linear fractional action of SL2(R), but it is oppressive to verify this directly. Worse, the goal is not merely to verify an expression presented as a deus ex machina, but, rather to systematically generate suitable expressions. An important part of this intention is understanding reasons for the existence of invariant operators, a...
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For two positive integers m and n, we let Pn be the open convex cone in R consisting of positive definite n × n real symmetric matrices and let R be the set of all m×n real matrices. In this article, we investigate differential operators on the non-reductive manifold Pn × R (m,n) that are invariant under the natural action of the semidirect product group GL(n,R)⋉R on the MinkowskiEuclid space P...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2021
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196721500296