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On the wildness of cambrian lattices

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arxiv 1704.01861 v1 pith:JUXWN54K submitted 2017-04-06 math.RT math.CO

Frédéric Chapoton (IRMA) , Baptiste Rognerud (IRMA) This is my paper · ORCID
classification math.RTmath.CO
keywords latticestyperepresentationgroupcambriancoxeterotherwhen
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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 3 1 , the lattices are of tame representation type. In all the other cases they are of wild representation type.

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