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On pointwise conjugacy of distinguished coset representatives in Coxeter groups

Fleischmann, Peter (2002) On pointwise conjugacy of distinguished coset representatives in Coxeter groups. Journal of Group Theory, 5 (3). pp. 269-283. ISSN 1433-5883. (doi:10.1515/jgth.2002.002) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:522)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL:
http://dx.doi.org/10.1515/jgth.2002.002

Abstract

Let (W, S) be a Coxeter system. For a standard parabolic. subgroup W-K,

K subset of or equal to S let D-K be the set of distinguished coset

representatives, i.e. representatives of cosets W(K)w of minimal

Coxeter length. If L = K-c subset of or equal to S with c is an element

of W, then D-K and D-L = c(-1) D-K are in general not conjugate as

sets. However it is shown that if WK is finite, they are conjugate

'pointwise', i.e. there is a bijection theta : D-K --> D-L such that

theta(d) = d(wc) for some w is an element of W-K depending on d is an

element of D-K. In particular for each conjugacy class C of W the

cardinalities # (D-K boolean AND C) and # (D-L boolean AND C) are the

same. The case of infinite standard parabolic subgroups is also

discussed and a corresponding result is proved.

Item Type: Article
DOI/Identification number: 10.1515/jgth.2002.002
Uncontrolled keywords: Subgroups
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:18 UTC
Last Modified: 16 Nov 2021 09:39 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/522 (The current URI for this page, for reference purposes)

University of Kent Author Information

Fleischmann, Peter.

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