On The Weak Order Of Orthogonal Groups

Annette Pilkington

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arXiv · 1110.4424

On The Weak Order Of Orthogonal Groups

Annette Pilkington

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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.

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Annette Pilkington. 2011-10-20. On The Weak Order Of Orthogonal Groups. https://arxiv.org/abs/1110.4424

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