Infinite Reduced Words, Lattice Property And Braid Graph of Affine Weyl Groups
Representation Theory
2019-07-26 v2 Combinatorics
Group Theory
Abstract
In this paper, we establish a bijection between the infinite reduced words of an affine Weyl group and certain biclosed sets of its positive system and determine all finitely generated biclosed sets in the positive system of an affine Weyl group. Using these results, we show first that the biclosed sets in the standard positive system of rank 3 affine Weyl groups when ordered by inclusion form a complete algebraic ortholattice and secondly that the (generalized) braid graphs of those Coxeter groups are connected, which can be thought of as an infinite version of Tit's solution to the word problem.
Keywords
Cite
@article{arxiv.1803.03017,
title = {Infinite Reduced Words, Lattice Property And Braid Graph of Affine Weyl Groups},
author = {Weijia Wang},
journal= {arXiv preprint arXiv:1803.03017},
year = {2019}
}
Comments
39 pages, a few corrections and additions after referee's report