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) |

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