Deficient homomorphisms between generalized Verma modules

2019 ◽  
Vol 30 (11) ◽  
pp. 1950056
Author(s):  
Anthony C. Kable
Keyword(s):  
Necessary Condition ◽  
Verma Modules ◽  
Parabolic Subalgebra ◽  
Generalized Verma Modules

A class of homomorphisms between generalized Verma modules that have an unusual degeneracy is identified. Homomorphisms in this class are called deficient homomorphisms. A family of maximally deficient homomorphisms is constructed. A necessary condition on a parabolic subalgebra is identified for the associated category of generalized Verma modules to admit deficient homomorphisms.

Structure of Modules Induced from Simple Modules with Minimal Annihilator

2004 ◽  
Vol 56 (2) ◽  
pp. 293-309 ◽  
Author(s):  
Oleksandr Khomenko ◽  
Volodymyr Mazorchuk
Keyword(s):  
Simple Module ◽  
Verma Modules ◽  
Simple Complex ◽  
Parabolic Subalgebra ◽  
Simple Modules ◽  
Finite Dimensional ◽  
Levi Factor ◽  
Generalized Verma Modules ◽  
Primitive Ideals ◽  
Irreducibility Criterion

AbstractWe study the structure of generalized Verma modules over a semi-simple complex finite-dimensional Lie algebra, which are induced from simple modules over a parabolic subalgebra. We consider the case when the annihilator of the starting simple module is a minimal primitive ideal if we restrict this module to the Levi factor of the parabolic subalgebra. We show that these modules correspond to proper standard modules in some parabolic generalization of the Bernstein-Gelfand-Gelfand category and prove that the blocks of this parabolic category are equivalent to certain blocks of the category of Harish-Chandra bimodules. From this we derive, in particular, an irreducibility criterion for generalized Verma modules. We also compute the composition multiplicities of those simple subquotients, which correspond to the induction from simple modules whose annihilators are minimal primitive ideals.

scholarly journals SINGULAR VECTORS OF THE TOPOLOGICAL CONFORMAL ALGEBRA

1996 ◽  
Vol 11 (25) ◽  
pp. 4597-4621 ◽  
Author(s):  
A. M. SEMIKHATOV ◽  
I. YU. TIPUNIN
Keyword(s):  
General Formula ◽  
Singular Vector ◽  
Conformal Algebra ◽  
General Construction ◽  
Verma Modules ◽  
Recursion Relations ◽  
Singular Vectors ◽  
Generalized Verma Modules ◽  
New Construction ◽  
A Chain

A general construction is found for “topological” singular vectors of the twisted N=2 superconformal algebra. It demonstrates many parallels with the known construction for affine sℓ(2) singular vectors due to Malikov–Feigin–Fuchs, but is formulated independently of the latter. The two constructions taken together provide an isomorphism between the topological and affine sℓ(2) singular vectors. The general formula for topological singular vectors can be reformulated as a chain of direct recursion relations that allow one to derive a given singular vector | S(r, s)〉 from the lower ones | S(r, s′<s)〉. We also introduce generalized Verma modules over the twisted N=2 algebra and show that they provide a natural setup for the new construction for topological singular vectors.

scholarly journals Cycles Cohomology and Geometrical Correspondences of Derived Categories to Field Equations

2018 ◽  
Vol 14 (2) ◽  
pp. 7880-7892
Author(s):  
Francisco Bulnes
Keyword(s):  
Differential Operators ◽  
Derived Categories ◽  
Space Time ◽  
Verma Modules ◽  
Field Equations ◽  
Langlands Correspondence ◽  
Moduli Stacks ◽  
Generalized Verma Modules ◽  
Moduli Stack ◽  
Holomorphic Bundles

The integral geometry methods are the techniques could be the more naturally applied to study of the characterization of the moduli stacks and solution classes (represented cohomologically) obtained under the study of the kernels of the differential operators of the corresponding field theory equations to the space-time. Then through a functorial process a classification of differential operators is obtained through of the co-cycles spaces that are generalized Verma modules to the space-time, characterizing the solutions of the field equations. This extension can be given by a global Langlands correspondence between the Hecke sheaves category on an adequate moduli stack and the holomorphic bundles category with a special connection (Deligne connection). Using the classification theorem given by geometrical Langlands correspondences are given various examples on the information that the geometrical invariants and dualities give through moduli problems and Lie groups acting.

scholarly journals Low Degree Morphisms of E(5, 10)-Generalized Verma Modules

2019 ◽  
Vol 23 (6) ◽  
pp. 2131-2165
Author(s):  
Nicoletta Cantarini ◽  
Fabrizio Caselli
Keyword(s):  
Verma Modules ◽  
Generalized Verma Modules ◽  
Low Degree
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