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. (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)

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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
Uncontrolled keywords: Subgroups
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 19 Dec 2007 18:18
Last Modified: 19 May 2014 13:28
Resource URI: https://kar.kent.ac.uk/id/eprint/522 (The current URI for this page, for reference purposes)
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