scholarly journals The GLn(q)-module structure of the symmetric algebra around the Steinberg module

2011 ◽  
Vol 227 (4) ◽  
pp. 1562-1584 ◽  
Author(s):  
Jinkui Wan ◽  
Weiqiang Wang
Keyword(s):  
Symmetric Algebra ◽  
Module Structure ◽  
Steinberg Module

scholarly journals Twisted Dickson–Mui invariants and the Steinberg module multiplicity

2011 ◽  
Vol 151 (1) ◽  
pp. 43-57 ◽  
Author(s):  
JINKUI WAN ◽  
WEIQIANG WANG
Keyword(s):  
Tensor Product ◽  
Linear Group ◽  
General Linear Group ◽  
Exterior Algebra ◽  
Symmetric Algebra ◽  
General Linear ◽  
Parabolic Subgroups ◽  
Steinberg Module ◽  
Finite General Linear Group

AbstractWe determine the invariants, with arbitrary determinant twists, of the parabolic subgroups of the finite general linear group GLn(q) acting on the tensor product of the symmetric algebra S•(V) and the exterior algebra ∧•(V) of the natural GLn(q)-module V. In addition, we obtain the graded multiplicity of the Steinberg module of GLn(q) in S•(V) ⊗ ∧•(V), twisted by an arbitrary determinant power.

On the Structure of a Class of Graded Modules Related to Symmetric Pairs

2006 ◽  
Vol 13 (02) ◽  
pp. 315-328 ◽  
Author(s):  
Gang Han
Keyword(s):  
Lie Algebra ◽  
Adjoint Representation ◽  
Exterior Algebra ◽  
Symmetric Algebra ◽  
Module Structure ◽  
Cartan Decomposition ◽  
Isotropy Representation ◽  
Semisimple Lie Algebra ◽  
Graded Modules ◽  
Special Case

Let [Formula: see text] be the Cartan decomposition of a real semisimple Lie algebra and [Formula: see text] be its complexification. Let [Formula: see text] be the corresponding isotropy representation, and the exterior algebra [Formula: see text] becomes a graded [Formula: see text]-module by extending ν. We study a graded [Formula: see text]-submodule C of [Formula: see text] and get two important decompositions of the [Formula: see text]-module [Formula: see text]. Let [Formula: see text] be the symmetric algebra over [Formula: see text]. Then [Formula: see text] also has an [Formula: see text]-module structure, which is [Formula: see text]-equivariant, and C is a space of generators for this module. Our results generalize Kostant's results in the special case that ν is the adjoint representation of a semisimple Lie algebra.

Effect of OCA properties on foldable AMOLED panel with a module structure

2019 ◽  
pp. 1627
Author(s):  
Yali Liu ◽  
Yongzhen Jia ◽  
Zhengzhou Liu ◽  
Di Wu ◽  
Haoqun Li ◽  
...  
Keyword(s):  
Module Structure

Algorithm for detecting module structure in complex networks based on node type

2009 ◽  
Vol 28 (10) ◽  
pp. 2590-2593
Author(s):  
Wei SHI ◽  
Zheng ZHAO ◽  
Gui-xiang XUE
Keyword(s):  
Complex Networks ◽  
Module Structure ◽  
Node Type

Design and Implementation of Information System of 3D City of Geotechnical Engineering

2014 ◽  
Vol 716-717 ◽  
pp. 521-524
Author(s):  
Qiong Luo
Keyword(s):  
Information System ◽  
City Planning ◽  
System Management ◽  
Module Structure ◽  
Management Technology ◽  
Function Modules ◽  
Database Technology ◽  
Geotechnical Information ◽  
The City ◽  
Further Development

To meet the demand for the geotechnical information system management, this paper has put forward a plan to develop the management information system by using GIS and commercial database management technology. It has also described and analyzed the development of the function modules of the system and designed its module structure architecture for further development of the system. The GIS and database technology may be applied in managing, analyzing and evaluating the sea-volume geotechnical information data and help realize information sharing and provide policy-making support for the city planning, construction and management.

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