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arXiv:1912.02840 [math.RT]AbstractReferencesReviewsResources

Cambrian combinatorics on quiver representations (type A)

Emily Barnard, Emily Gunawan, Emily Meehan, Ralf Schiffler

Published 2019-12-05Version 1

This paper presents a new geometric model of the Auslander-Reiten quiver of a type A quiver. We introduce a new Catalan object which we call a maximal almost rigid representation. We show that its endomorphism algebra is a tilted algebra of type A. We define a partial order on the set of maximal almost rigid representations and use our new geometric model to show that this partial order is a Cambrian lattice.

Comments: 22 pages, 14 figures. Comments are welcome
Categories: math.RT, math.CO, math.RA
Subjects: 05E10, 16G20, 16G70
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