scholarly journals RELATING TENSOR STRUCTURES ON REPRESENTATIONS OF GENERAL LINEAR AND SYMMETRIC GROUPS

2018 ◽  
Vol 23 (2) ◽  
pp. 437-461 ◽  
Author(s):  
UPENDRA KULKARNI ◽  
SHRADDHA SRIVASTAVA ◽  
K. V. SUBRAHMANYAM
Keyword(s):  
Symmetric Groups ◽  
General Linear

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.

scholarly journals On comparing the cohomology of general linear and symmetric groups

2001 ◽  
Vol 201 (2) ◽  
pp. 339-355 ◽  
Author(s):  
Alexander S. Kleshchev ◽  
Daniel K. Nakano
Keyword(s):  
Symmetric Groups ◽  
General Linear

On Translation Functors for General Linear and Symmetric Groups

2000 ◽  
Vol 80 (1) ◽  
pp. 75-106 ◽  
Author(s):  
Jonathan Brundan ◽  
Alexander Kleshchev
Keyword(s):  
Symmetric Groups ◽  
General Linear
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