Abstract.
Let W be the Weyl group of a connected reductive group over a finite field. It is a consequence of the Borel-Tits rational conjugacy theorem for maximal split tori that for certain reflection subgroups W 1 of W (including all parabolic subgroups), the elements of minimal reflection length in any coset wW 1 are all conjugate, provided w normalises W 1. We prove a sharper and more general result of this nature for any finite Coxeter group. Applications include a fusion result for cosets of reflection subgroups and the counting of rational orbits of a given type in reductive Lie algebras over finite fields.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: 27.10.1998
Rights and permissions
About this article
Cite this article
B. Howlett, R., I. Lehrer, G. On reflection length in reflection groups. Arch. Math. 73, 321–326 (1999). https://doi.org/10.1007/s000130050404
Issue Date:
DOI: https://doi.org/10.1007/s000130050404