Fabrizio Caselli ; Roberta Fulci - Models and refined models for involutory reflection groups and classical Weyl groups

dmtcs:2864 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2864
Models and refined models for involutory reflection groups and classical Weyl groupsArticle

Authors: Fabrizio Caselli 1; Roberta Fulci 1

  • 1 Dipartimento di Matematica [Bologna]

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.


Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Complex reflection groups,Gelfand models,Classical Weyl groups,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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