scholarly journals Book Review: Schur algebras and representation theory

1996 ◽  
Vol 33 (03) ◽  
pp. 371-376
Author(s):  
Brian Parshall
Keyword(s):  
Representation Theory ◽  
Schur Algebras

Cellular bases of generalised q-Schur algebras

2016 ◽  
Vol 162 (3) ◽  
pp. 533-560
Author(s):  
STEPHEN DOTY ◽  
ANTHONY GIAQUINTO
Keyword(s):  
Representation Theory ◽  
Finite Type ◽  
Basic Structure ◽  
Schur Algebras ◽  
Generators And Relations

AbstractStarting from their defining presentation by generators and relations, we develop the basic structure and representation theory of generalised q-Schur algebras of finite type.

scholarly journals Young modules for symmetric groups

2001 ◽  
Vol 71 (2) ◽  
pp. 201-210 ◽  
Author(s):  
Karin Erdmann
Keyword(s):  
Representation Theory ◽  
Finite Groups ◽  
Symmetric Groups ◽  
General Linear ◽  
Linear Groups ◽  
Schur Algebras ◽  
General Linear Groups ◽  
Green Correspondence

AbstractLet K be a field of characteristic p. The permutation modules associated to partitions of n, usually denoted as Mλ, play a central role not only for symmetric groups but also for general linear groups, via Schur algebras. The indecomposable direct summands of these Mλ were parametrized by James; they are now known as Young modules; and Klyachko and Grabmeier developed a ‘Green correspondence’ for Young modules. The original parametrization used Schur algebras; and James remarked that he did not know a proof using only the representation theory of symmetric groups. We will give such proof, and we will at the same time also prove the correspondence result, by using only the Brauer construction, which is valid for arbitrary finite groups.

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