Exceptional sequences of type Bn/Cn and those in the abelian tube
Abstract
We examine clusters in the cluster tube of rank n+1 using exceptional sequences in the abelian tube of rank n+1. Although the abelian tube has more exceptional sequences than the module categories of type Bn/Cn, we obtain a bijection between the set of signed exceptional sequences of any length in these categories. This bijection gives a reinterpretation of the formula of Buan-Marsh-Vatne comparing clusters of type Bn/Cn with maximal rigid objects in the cluster tube of rank n+1. The bijection passes through the set of "augmented" rooted labeled trees.
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