Letter Place Algebras and a Characteristic-Free Approach to the Representation Theory of the General Linear and Symmetric Groups, I

1982 ◽  
pp. 197-253
Author(s):  
MICHAEL CLAUSEN
Keyword(s):  
Representation Theory ◽  
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 STABILITY PATTERNS IN REPRESENTATION THEORY

2015 ◽  
Vol 3 ◽  
Author(s):  
STEVEN V SAM ◽  
ANDREW SNOWDEN
Keyword(s):  
Representation Theory ◽  
Linear Theory ◽  
Symmetric Groups ◽  
General Linear ◽  
Stable Category ◽  
Comprehensive Theory ◽  
Stable Representation

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is an array of equivalences between the stable representation category and various other categories, each of which has its own flavor (representation theoretic, combinatorial, commutative algebraic, or categorical) and offers a distinct perspective on the stable category. We use this theory to produce a host of specific results: for example, the construction of injective resolutions of simple objects, duality between the orthogonal and symplectic theories, and a canonical derived auto-equivalence of the general linear theory.

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
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