Powers of Coxeter elements in infinite groups are reduced

Author:
David E. Speyer

Journal:
Proc. Amer. Math. Soc. **137** (2009), 1295-1302

MSC (2000):
Primary 20F55

DOI:
https://doi.org/10.1090/S0002-9939-08-09638-X

Published electronically:
October 29, 2008

MathSciNet review:
2465651

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an infinite irreducible Coxeter group with the simple generators. We give a short proof that the word is reduced for any number of repetitions of . This result was proved for simply laced, crystallographic groups by Kleiner and Pelley using methods from the theory of quiver representations. Our proof uses only basic facts about Coxeter groups and the geometry of root systems. We also prove that, in finite Coxeter groups, there is a reduced word for which is obtained from the semi-infinite word by interchanging commuting elements and taking a prefix.

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Additional Information

**David E. Speyer**

Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachu- setts Avenue, Cambridge, Massachusetts 02139

Email:
speyer@math.mit.edu

DOI:
https://doi.org/10.1090/S0002-9939-08-09638-X

Received by editor(s):
February 11, 2008

Received by editor(s) in revised form:
May 8, 2008

Published electronically:
October 29, 2008

Communicated by:
Jim Haglund

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.