On The Weak Order Of Orthogonal Groups
Group Theory
2011-10-21 v1
Abstract
A structure of a complete lattice (in the sense of a poset) is defined on the underlying set of the orhtogonal group of a real Euclidean space, by a construction analogous to that of the weak order of a Coxeter system in terms of its root system. This gives rise to a complte rootoid in the sense of Dyer, with the orthogonal group as underlying group.
Cite
@article{arxiv.1110.4424,
title = {On The Weak Order Of Orthogonal Groups},
author = {Annette Pilkington},
journal= {arXiv preprint arXiv:1110.4424},
year = {2011}
}
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15 Pages