Homomorphisms of Semiholonomic Verma Modules: an Exceptional Case
نویسندگان
چکیده
It is well known that Verma module homomorphisms correspond to invariant operators on homogeneous spaces, which in certain situations can be regarded as the flat models of specific differential geometries. This can be generalised to curved space by introducing semiholonomic Verma modules, whose homomorphisms give rise to invariant operators on curved space. In this article we investigate from a purely algebraic point of view which Verma module homomorphisms lift to the semiholonomic case for the exceptional Lie algebra E6.
منابع مشابه
Constructing homomorphisms between Verma modules
We describe a practical method for constructing a nontrivial homomorphism between two Verma modules of an arbitrary semisimple Lie algebra. With some additions the method generalises to the affine case. A theorem of Verma, Bernstein-Gel’fand-Gel’fand gives a straightforward criterion for the existence of a nontrivial homomorphism between Verma modules. Moreover, the theorem states that such hom...
متن کاملOn natural homomorphisms of local cohomology modules
Let $M$ be a non-zero finitely generated module over a commutative Noetherian local ring $(R,mathfrak{m})$ with $dim_R(M)=t$. Let $I$ be an ideal of $R$ with $grade(I,M)=c$. In this article we will investigate several natural homomorphisms of local cohomology modules. The main purpose of this article is to investigate when the natural homomorphisms $gamma: Tor^{R}_c(k,H^c_I(M))to kotim...
متن کاملHomomorphisms between Verma Modules in Characteristic P
Let g be a complex semisimple Lie algebra, with a Bore1 subalgebra b c g and Cartan subalgebra h c b. In classifying the finite dimensional representations of g, Cartan showed that any simple finite dimensional g-module has a generating element u, annihilated by n = [b, b], on which h acts by a linear form I E h*. Such an element is called a primitive vector (for the module). Harish-Chandra [9]...
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 کاملModules of the toroidal Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$
Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a new triangular decomposition. Singular vectors of Verma modules are determined using a similar condition with horizontal affine Lie subalgebras, and highest weight modules are described under the condition $c_1>0$ and $c_2=0$.
متن کامل