Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2510.16177 |
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Inhaltsangabe:
- Noncrossing partition posets in a Coxeter group $W$ can fail to be lattices when $W$ is not finite. When the lattice property fails for $W$ of affine type, McCammond and Sulway's construction provides a larger lattice that contains the noncrossing partition poset and that furthermore is a combinatorial Garside structure. We construct a lattice, isomorphic to McCammond and Sulway's lattice, using the representation theory of a corresponding connected tame hereditary algebra and give a representation-theoretic proof that it is a combinatorial Garside structure. To construct the lattice, we introduce para-exceptional sequences and para-exceptional subcategories in the module categories of tame hereditary algebras. Para-exceptional sequences are generalizations of exceptional sequences obtained by enlarging the set of allowed entries to include all non-homogeneous bricks. A para-exceptional subcategory is a subcategory obtained by applying a certain closure-like operator to the wide subcategory generated by a para-exceptional sequence.