Tensor products and dimensions of simple modules for symmetric groups

1995 ◽  
Vol 88 (1) ◽  
pp. 357-386 ◽  
Author(s):  
Karin Erdmann
Keyword(s):  
Symmetric Groups ◽  
Tensor Products ◽  
Simple Modules

The Vertices of a Class of Specht Modules and Simple Modules for Symmetric Groups in Characteristic 2

2012 ◽  
Vol 19 (spec01) ◽  
pp. 987-1016 ◽  
Author(s):  
Susanne Danz ◽  
Karin Erdmann
Keyword(s):  
Symmetric Groups ◽  
Specht Modules ◽  
Simple Modules ◽  
Characteristic 2

We study Specht modules S(n-2,2) and simple modules D(n-2,2) for symmetric groups 𝔖n of degree n over a field of characteristic 2. In particular, we determine the vertices of these modules, and also provide some information on their sources.

scholarly journals A note on vertices of indecomposable tensor products

2020 ◽  
Vol 23 (3) ◽  
pp. 385-391
Author(s):  
Markus Linckelmann
Keyword(s):  
Finite Group ◽  
Group Algebra ◽  
Present Note ◽  
Tensor Products ◽  
Solvable Groups ◽  
Sufficient Criterion ◽  
Indecomposable Modules ◽  
Main Motivation ◽  
Simple Modules ◽  
A Finite Group

AbstractG. Navarro raised the question of when two vertices of two indecomposable modules over a finite group algebra generate a Sylow p-subgroup. The present note provides a sufficient criterion for this to happen. This generalises a result by Navarro for simple modules over finite p-solvable groups, which is the main motivation for this note.

Truncated symmetric powers and modular representations of GLn

1996 ◽  
Vol 119 (2) ◽  
pp. 231-242 ◽  
Author(s):  
Stephen Doty ◽  
Grant Walker
Keyword(s):  
General Linear Group ◽  
Schur Functions ◽  
Tensor Products ◽  
Modular Representation ◽  
Modular Representations ◽  
Modular Representation Theory ◽  
Simple Modules ◽  
Symmetric Powers ◽  
Natural Module ◽  
Natural Way

AbstractSeveral results are obtained relating to the modular representation theory of the general linear group GLn in the defining characteristic p > 0. In Section 1, embeddings of certain simple modules in symmetric powers of the natural module, or in tensor products of truncated symmetric powers, are constructed. In Section 2, cases are found where simple quotientsof Schur modules H0(λ) can be constructed by extending theidea of truncation to these modules in a natural way. In Section 3, the characters of those simple modules which can be constructed as twisted tensor products of truncated symmetric powers are expressed in terms of Schur functions.

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