Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0757.20003
Baddeley, R.W.
Models and involution models for wreath products and certain Weyl groups. (English)
[J] J. Lond. Math. Soc., II. Ser. 44, No.1, 55-74 (1991). ISSN 0024-6107; ISSN 1469-7750/e

A model for the irreducible complex representations of a group $G$ is a set $M=\{\rho\sb 1,\dots,\rho\sb m\}$, where $\rho\sb i: G\sb i\to\bbfC$ are linear representations of subgroups of $G$ such that $\sum\sp m\sb{i=1}\rho\sp G\sb i=\sum\sb{\rho\in \text{Irr.}G}\rho$. In particular we say that $M$ is an involution model on $E=\{e\sb 1,\dots,e\sb m\}\subseteq G$ if the following hold: $G\sb i=C\sb G(e\sb i)$, $i=1,\dots,m$, $\{g\in G: g\sp 2=1\}=\prod\sp m\sb{i=1}\{e\sb i\sp g: g\in G\}$. Similar models are known to exist for the Weyl groups of type $B\sb n$ for all $n$, and type $D\sb n$ for $n$ odd. The main result of this paper is to obtain the following generalization to wreath products. Theorem: If a group $H$ has an involution model so does $H\text{ wr }S\sb n$. In this paper the author shows that the Weyl group of type $D\sb 4$ $((S\sb 2\text{ wr }S\sb n)\cap A\sb 8)$ does not have an involution model and he gives a general result on models which gives a model for any of the Weyl groups of type $D\sb n$.
[P.Lakatos (Debrecen)]

MSC 2000:: *20E22 Extensions and other compositions of groups
20C33 Representations of finite groups of Lie type
20C15 Ordinary representations and characters of groups

Keywords: irreducible complex representations; linear representations; Weyl groups; wreath products; involution model

Cited in: Zbl pre06127521

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]