Generalized Verma Modules
نویسنده
چکیده
منابع مشابه
On multiplicities of simple subquotients in Generalized Verma modules
We reduce the problem on multiplicities of simple subquotients in an-stratiied Generalized Verma module to the analogous problem for classical Verma modules.
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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...
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The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras Lie G2 i ↪→ so(7), and generalized conformal so(7)-Verma modules of scalar type. As a result, we classify t...
متن کاملQuantum coadjoint orbits of GL(n) and generalized Verma modules
In our previous paper, we constructed an explicit GL(n)-equivariant quantization of the Kirillov–Kostant-Souriau bracket on a semisimple coadjoint orbit. In the present paper, we realize that quantization as a subalgebra of endomorphisms of a generalized Verma module. As a corollary, we obtain an explicit description of the annihilators of generalized Verma modules over U (
متن کاملVerma modules over the generalized Heisenberg-Virasoro algebra
For any additive subgroup G of an arbitrary field F of characteristic zero, there corresponds a generalized Heisenberg-Virasoro algebra L[G]. Given a total order of G compatible with its group structure, and any h, hI , c, cI , cLI ∈ F, a Verma module M̃(h, hI , c, cI , cLI) over L[G] is defined. In the this note, the irreducibility of Verma modules M̃(h, hI , c, cI , cLI) is completely determined.
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 $c_2=0$.
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تاریخ انتشار 1999