Finite-dimensional representations of invariant differential operators
نویسندگان
چکیده
منابع مشابه
Dimensional Reduction of Invariant Fields and Differential Operators. II. Reduction of Invariant Differential Operators
In the present paper, which is a sequel of [1], we consider the dimensional reduction of differential operators (DOs) that are invariant with respect to the action of a connected Lie group G. The action of G on vector bundles induces naturally actions of G on their sections and on the DOs between them. In [1] we constructed explicitly the reduced bundle ξ, such that the set of all its sections,...
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It is known that the algebra D(V ) of G-invariant differential operators corresponding to a G-module V of a complex reductive group G is commutative if and only if V is a spherical G-module. In the present work we study the structure of D(V ) for G-modules with spherical orbits. It is proved that the centralizer Z(V ) of the subalgebra k[V ] in D(V ) is commutative. Also a characterization of a...
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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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Problems related to symmetries and dimensional reduction are common in the mathematical and physical literature, and are intensively studied presently. As a rule, the symmetry group (“reducing group”) and its orbits (“external dimensions”) are compact, and this is essential in models where the volume of the orbits is related to physical quantities. But this case is only a part of the natural pr...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2002
ISSN: 0021-8693
DOI: 10.1016/s0021-8693(02)00500-8