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Article Dans Une Revue Communications in Algebra Année : 2018

Coxeter groups, symmetries, and rooted representations

Résumé

Let $G$ be a group of symmetries of a Coxeter system $(W,S)$ and let $f:W \to GL (V)$ be the linear representation associated with a root basis $(V, \langle .,. \rangle, \Pi)$. We show that $W^G$ is a Coxeter group, we construct a subset $\tilde \Pi \subset V^G$ so that $(V^G, \langle .,. \rangle, \tilde \Pi)$ is a root basis of $W^G$, and we show that the induced representation $f^G : W^G \to GL( V^G)$ is the linear representation associated with $(V^G, \langle .,. \rangle, \tilde \Pi)$. In particular, the latter is faithful.
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Dates et versions

hal-01404050 , version 1 (28-11-2016)

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Olivier Geneste, Luis Paris. Coxeter groups, symmetries, and rooted representations. Communications in Algebra, 2018, 46 (5), pp.1996-2002. ⟨10.1080/00927872.2017.1363221⟩. ⟨hal-01404050⟩
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