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On the Wildness of Cambrian Lattices

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Abstract

In this note, we investigate the representation type of the cambrian lattices and some other related lattices. The result is expressed as a very simple trichotomy. When the rank of the underlined Coxeter group is at most 2, the lattices are of finite representation type. When the Coxeter group is a reducible group of type \({\mathbb {A}_{1}^{3}}\), the lattices are of tame representation type. In all the other cases they are of wild representation type.

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Authors and Affiliations

  1. Institut de Recherche Mathématique Avancée, CNRS UMR 7501, Université de Strasbourg, F-67084, Strasbourg Cedex, France

    Frédéric Chapoton & Baptiste Rognerud

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  1. Frédéric Chapoton
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  2. Baptiste Rognerud
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Correspondence to Baptiste Rognerud.

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Presented by: Yuri Drozd

Le premier auteur abénéficié d’une aide de l’Agence Nationale de la Recherche (projet Carma, référence ANR-12-BS01-0017).

Le second auteur a bénéficié d’un financement de l’IDEX BMM/PN/AM/N∘ 2016-096c.

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Chapoton, F., Rognerud, B. On the Wildness of Cambrian Lattices. Algebr Represent Theor 22, 603–614 (2019). https://doi.org/10.1007/s10468-018-9789-1

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