Noncrossing partitions and representations of quivers

Ingalls, Colin et Thomas, Hugh (2009). « Noncrossing partitions and representations of quivers ». Compositio Mathematica, 145(06), p. 1533.

Fichier(s) associé(s) à ce document :

Prévisualisation	PDF Télécharger (327kB)

Résumé

We situate the noncrossing partitions associated with a finite Coxeter group within the context of the representation theory of quivers. We describe Reading’s bijection between noncrossing partitions and clusters in this context, and show that it extends to the extended Dynkin case. Our setup also yields a new proof that the noncrossing partitions associated with a finite Coxeter group form a lattice. We also prove some new results within the theory of quiver representations. We show that the finitely generated, exact abelian, and extension-closed subcategories of the representations of a quiver Q without oriented cycles are in natural bijection with the cluster tilting objects in the associated cluster category. We also show that these subcategories are exactly the finitely generated categories that can be obtained as the semistable objects with respect to some stability condition.

Type:	Article de revue scientifique
Mots-clés ou Sujets:	noncrossing partitions; Dynkin quivers; reflections groups; cluster category; quiver representations; torsion class; wide subcategories; Cambrian lattice; semistable subcategories
Unité d'appartenance:	Faculté des sciences > Département de mathématiques
Déposé par:	Hugh R. Thomas
Date de dépôt:	18 mai 2016 19:50
Dernière modification:	30 mai 2016 20:14
Adresse URL :	http://archipel.uqam.ca/id/eprint/8490

Modifier les métadonnées (propriétaire du document)

Statistiques