Reducibility of generalized Verma modules for Hermitian symmetric pairs

2021 ◽  
Vol 225 (4) ◽  
pp. 106561
Author(s):  
Zhanqiang Bai ◽  
Wei Xiao
Keyword(s):  
Verma Modules ◽  
Generalized Verma Modules

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

Tensor Products of Holomorphic Discrete Series Representations

1979 ◽  
Vol 31 (4) ◽  
pp. 836-844 ◽  
Author(s):  
Joe Repka
Keyword(s):  
Discrete Series ◽  
Tensor Products ◽  
Holomorphic Functions ◽  
Verma Modules ◽  
Holomorphic Discrete Series ◽  
Spaces Of Holomorphic Functions ◽  
Highest Weight ◽  
Generalized Verma Modules ◽  
Series Representations ◽  
Discrete Series Representations

We discuss the decomposition of tensor products of holomorphic discrete series representations, generalizing a technique used in [9] for representations of SL2(R), based on a suggestion of Roger Howe. In the case of two representations with highest weights, the discussion is entirely algebraic, and is best formulated in the context of generalized Verma modules (see § 3). In the case when one representation has a highest weight and the other a lowest weight, the approach is more analytic, relying on the realization of these representations on certain spaces of holomorphic functions.For a simple group, these two cases exhaust the possibilities; for a nonsimple group, one has to piece together representations on the various factors.The author wishes to thank Roger Howe and Jim Lepowsky for very helpful conversations, and Nolan Wallach for pointing out the work of Eugene Gutkin (Thesis, Brandeis University, 1978), from which some of the results of this paper can be read off as easy corollaries.

Sign in / Sign up

Export Citation Format

Share Document