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:https://doi.org/10.1515/jgth.2002.002)
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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 > Sciences > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Judith Broom |

Date Deposited: | 19 Dec 2007 18:18 UTC |

Last Modified: | 19 May 2014 13:28 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/522 (The current URI for this page, for reference purposes) |

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