On The Weak Order Of Orthogonal Groups

Details On The Weak Order Of Orthogonal Groups On The Weak Order Of Orthogonal Groups

2011-10-20

arxiv.org/abs/1110.4424v1

Mathematics

Group Theory

15 Pages

Scientific paper

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.

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