Exceptional sequences of type $B_n/C_n$ and those in the abelian tube
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915503548661760 |
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| author | Igusa, Kiyoshi Sen, Emre |
| author_facet | Igusa, Kiyoshi Sen, Emre |
| contents | 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 $B_{n}/C_{n}$, 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 $B_n/C_n$ with maximal rigid objects in the cluster tube of rank $n+1$. The bijection passes through the set of "augmented" rooted labeled trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01700 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Exceptional sequences of type $B_n/C_n$ and those in the abelian tube Igusa, Kiyoshi Sen, Emre Representation Theory Combinatorics 16G20: 05C05 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 $B_{n}/C_{n}$, 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 $B_n/C_n$ with maximal rigid objects in the cluster tube of rank $n+1$. The bijection passes through the set of "augmented" rooted labeled trees. |
| title | Exceptional sequences of type $B_n/C_n$ and those in the abelian tube |
| topic | Representation Theory Combinatorics 16G20: 05C05 |
| url | https://arxiv.org/abs/2310.01700 |