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arXiv · 2510.16177

Para-exceptional sequences for tame hereditary algebras and McCammond-Sulway lattices

Eric J. Hanson·Nathan Reading
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Abstract

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.

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BibTeXRIS

Eric J. Hanson, Nathan Reading. 2025-10-17. Para-exceptional sequences for tame hereditary algebras and McCammond-Sulway lattices. https://arxiv.org/abs/2510.16177

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