On the wildness of cambrian lattices

Frédéric Chapoton (1) , Baptiste Rognerud (1)

1 IRMA - Institut de Recherche Mathématique Avancée

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 $A_{1}^{3}$ , the lattices are of tame representation type. In all the other cases they are of wild representation type.

Keywords: Cambrian lattice; Poset; Representation type

Domains: Representation Theory [math.RT]; Combinatorics [math.CO]

Frédéric Chapoton, Baptiste Rognerud. On the wildness of cambrian lattices. Algebras and Representation Theory, 2018. ⟨hal-01503158⟩