On the representation theory of wreath products of finite groups and symmetric groups

1999 ◽  
Vol 96 (5) ◽  
pp. 3590-3599 ◽  
Author(s):  
I. A. Pushkarev
Keyword(s):  
Representation Theory ◽  
Finite Groups ◽  
Symmetric Groups ◽  
Wreath Products

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

2009 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Finite Groups ◽  
Wreath Products

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.

Representation theory of wreath products of finite groups

2008 ◽  
Vol 156 (1) ◽  
pp. 44-55 ◽  
Author(s):  
T. Ceccherini-Silberstein ◽  
F. Scarabotti ◽  
F. Tolli
Keyword(s):  
Representation Theory ◽  
Finite Groups ◽  
Wreath Products

scholarly journals Character theory of infinite wreath products

2005 ◽  
Vol 2005 (9) ◽  
pp. 1365-1379 ◽  
Author(s):  
Robert Boyer
Keyword(s):  
Representation Theory ◽  
Symmetric Group ◽  
Finite Groups ◽  
Wreath Products ◽  
Character Theory ◽  
Group Algebras ◽  
Inductive Limits ◽  
Infinite Symmetric Group ◽  
The Relationship ◽  
Asymptotic Character

The representation theory of infinite wreath product groups is developed by means of the relationship between their group algebras and conjugacy classes with those of the infinite symmetric group. Further, since these groups are inductive limits of finite groups, their finite characters can be classified as limits of normalized irreducible characters of prelimit finite groups. This identification is called the “asymptotic character formula.” TheK0-invariant of the groupC∗-algebra is also determined.

scholarly journals ON THE REGULARITY CONJECTURE FOR THE COHOMOLOGY OF FINITE GROUPS

2008 ◽  
Vol 51 (2) ◽  
pp. 273-284 ◽  
Author(s):  
David J. Benson
Keyword(s):  
Finite Group ◽  
Wreath Product ◽  
Finite Groups ◽  
Cohomology Ring ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Characteristic P ◽  
Residue Classes ◽  
The Difference ◽  
A Finite Group

AbstractLet $K$ be a field of characteristic $p$ and let $G$ be a finite group of order divisible by $p$. The regularity conjecture states that the Castelnuovo–Mumford regularity of the cohomology ring $H^*(G,K)$ is always equal to 0. We prove that if the regularity conjecture holds for a finite group $H$, then it holds for the wreath product $H\wr\mathbb{Z}/p$. As a corollary, we prove the regularity conjecture for the symmetric groups $\varSigma_n$. The significance of this is that it is the first set of examples for which the regularity conjecture has been checked, where the difference between the Krull dimension and the depth of the cohomology ring is large. If this difference is at most 2, the regularity conjecture is already known to hold by previous work.For more general wreath products, we have not managed to prove the regularity conjecture. Instead we prove a weaker statement: namely, that the dimensions of the cohomology groups are polynomial on residue classes (PORC) in the sense of Higman.

scholarly journals Dual Graded Graphs and Bratteli Diagrams of Towers of Groups

10.37236/7790 ◽  
2019 ◽  
Vol 26 (1) ◽  
Author(s):  
Christian Gaetz
Keyword(s):  
Finite Groups ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Critical Groups ◽  
Bratteli Diagrams ◽  
Graded Graph ◽  
Differential Poset ◽  
Dual Graded Graphs ◽  
Nested Sequence ◽  
Special Case

An $r$-dual tower of groups is a nested sequence of finite groups, like the symmetric groups, whose Bratteli diagram forms an $r$-dual graded graph.  Miller and Reiner introduced a special case of these towers in order to study the Smith forms of the up and down maps in a differential poset.  Agarwal and the author have also used these towers to compute critical groups of representations of groups appearing in the tower.  In this paper I prove that when $r=1$ or $r$ is prime, wreath products of a fixed group with the symmetric groups are the only $r$-dual tower of groups, and conjecture that this is the case for general values of $r$.  This implies that these wreath products are the only groups for which one can define an analog of the Robinson-Schensted bijection in terms of a growth rule in a dual graded graph.

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