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arXiv · 1911.09865

Preprojective roots and cycle graphs

Yuji Komatsu
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Abstract

We study $c$-preprojective roots for a Coxeter element $c$ of infinite Coxeter group $W$. In particular, we consider the case when any positive root is $c$-preprojective for some Coxeter element $c$. In this paper, by assuming that the Coxeter graph of $W$ is cyclic, we establish that any positive root is $c$-preprojective for some Coxeter element $c$ if and only if $W$ is an affine Coxeter group.

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Yuji Komatsu. 2019-11-22. Preprojective roots and cycle graphs. https://arxiv.org/abs/1911.09865

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