Powers of Coxeter elements in infinite groups are reduced

Details Powers of Coxeter elements in infinite groups are reduced Powers of Coxeter elements in infinite groups are reduced

2007-10-16

arxiv.org/abs/0710.3188v1

Mathematics

Combinatorics

7 pages, no figures

Scientific paper

Let W be an infinite irreducible Coxeter group with (s_1, ..., s_n) the simple generators. We give a simple proof that the word s_1 s_2 ... s_n s_1 s_2 >... s_n ... s_1 s_2 ... s_n is reduced for any number of repetitions of s_1 s_2 >... s_n. This result was proved for simply-laced, crystallographic groups by Kleiner and Pelley using methods from the theory of quiver representations. Our proof only using basic facts about Coxeter groups and the geometry of root systems.

Affiliated with

Also associated with

No associations

Rating

Powers of Coxeter elements in infinite groups are reduced does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Powers of Coxeter elements in infinite groups are reduced, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Powers of Coxeter elements in infinite groups are reduced will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-11282