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On the Wildness of Cambrian Lattices

Authors
  • Chapoton, Frédéric
  • Rognerud, Baptiste
Type
Published Article
Journal
Algebras and Representation Theory
Publisher
Springer Netherlands
Publication Date
May 02, 2018
Volume
22
Issue
3
Pages
603–614
Identifiers
DOI: 10.1007/s10468-018-9789-1
Source
Springer Nature
Keywords
License
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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 A13\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathbb {A}_{1}^{3}}$\end{document}, the lattices are of tame representation type. In all the other cases they are of wild representation type.

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