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Models and refined models for involutory reflection groups and classical Weyl groups

Abstract : A finite subgroup $G$ of $GL(n,\mathbb{C})$ is involutory if the sum of the dimensions of its irreducible complex representations is given by the number of absolute involutions in the group, i.e. elements $g \in G$ such that $g \bar{g}=1$, where the bar denotes complex conjugation. A uniform combinatorial model is constructed for all non-exceptional irreducible complex reflection groups which are involutory including, in particular, all infinite families of finite irreducible Coxeter groups. If $G$ is a classical Weyl group this result is much refined in a way which is compatible with the Robinson-Schensted correspondence on involutions.
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Fabrizio Caselli, Roberta Fulci. Models and refined models for involutory reflection groups and classical Weyl groups. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.215-226. ⟨hal-01186293⟩

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