Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


A characterization of total reflection orders

Author: Paola Cellini
Journal: Proc. Amer. Math. Soc. 128 (2000), 1633-1639
MSC (1991): Primary 20F55; Secondary 05E99
Published electronically: October 27, 1999
MathSciNet review: 1653429
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $(W,S)$ be a Coxeter system with set of reflections $T$. It is known that if $\prec $ is a total reflection order for $W$, then, for each $s\in S$, $\{t\in T\mid t\prec s\}$ and its complement are stable under conjugation by $s$. Moreover the upper and lower $s$-conjugates of $\prec $ are still total reflection orders. For any total order $\prec $ on $T$, say that $\prec $ is stable if $\{t\in T\mid t\prec s\}$ is stable under conjugation by $s$ for each $s\in S$. We prove that if $\prec $ and all orders obtained from $\prec $ by successive lower or upper $S$-conjugations are stable, then $\prec $ is a total reflection order.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20F55, 05E99

Retrieve articles in all journals with MSC (1991): 20F55, 05E99

Additional Information

Paola Cellini
Affiliation: Dipartimento di Matematica Pura e Applicata, Università di Padova, Via Belzoni 7, 35131 Padova, Italy

PII: S 0002-9939(99)05234-X
Keywords: Coxeter groups, total reflection orders
Received by editor(s): July 30, 1998
Published electronically: October 27, 1999
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 2000 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia