Parabolic subgroup orbits on finite root systems

M. J. Dyer; G. I. Lehrer

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arXiv · 1708.00913

Parabolic subgroup orbits on finite root systems

M. J. Dyer·G. I. Lehrer

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Abstract

Oshima's Lemma describes the orbits of parabolic subgroups of irreducible finite Weyl groups on crystallographic root systems. This note generalises that result to all root systems of finite Coxeter groups, and provides a self contained proof, independent of the representation theory of semisimple complex Lie algebras.

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M. J. Dyer, G. I. Lehrer. 2017-08-02. Parabolic subgroup orbits on finite root systems. https://arxiv.org/abs/1708.00913

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