Verma modules and differential conformal invariants
نویسندگان
چکیده
منابع مشابه
New Generalized Verma Modules and Multilinear Intertwining Differential Operators
The present paper contains two interrelated developments. First are proposed new generalized Verma modules. They are called k Verma modules, k ∈ IN , and coincide with the usual Verma modules for k = 1. As a vector space a k Verma module is isomorphic to the symmetric tensor product of k copies of the universal enveloping algebra U(G), where G is the subalgebra of lowering generators in the sta...
متن کاملSystems of Differential Operators and Generalized Verma Modules
In this paper we close the cases that were left open in our earlier works on the study of conformally invariant systems of second-order differential operators for degenerate principal series. More precisely, for these cases, we find the special values of the systems of differential operators, and determine the standardness of the homomorphisms between the generalized Verma modules, that come fr...
متن کاملSemi–holonomic Verma Modules
Verma modules arise geometrically through the jets of homogeneous vector bundles. We consider in this article, the modules that arise from the semi-holonomic jets of a homogeneous vector bundle. We are particularly concerned with the case of a sphere under MMbius transformations. In this case there are immediate applications in the theory of conformally invariant diierential operators.
متن کاملVerma Modules of Critical Level and Differential Forms on Opers
Let g be a simple finite-dimensional Lie algebra and ĝκ, where κ is an invariant inner product on g, the corresponding affine Kac-Moody algebra. Consider the vacuum module Vκ over ĝκ (see Section 2 for the precise definitions). According to the results of [FF, Fr], the algebra of endomorphisms of Vκ is trivial, i.e., isomorphic to C, unless κ = κc, the critical value. The algebra Endĝκc Vκc is ...
متن کاملSelf-extensions of Verma Modules and Differential Forms on Opers
We compute the algebras of self-extensions of the vacuum module and the Verma modules over an affine Kac-Moody algebra ĝ in suitable categories of Harish-Chandra modules. We show that at the critical level these algebras are isomorphic to the algebras of differential forms on various spaces of opers associated to the Langlands dual Lie algebra of g, whereas away from the critical level they bec...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1990
ISSN: 0022-040X
DOI: 10.4310/jdg/1214445537