Categorification of a frieze pattern determinant
Combinatorics
2020-12-21 v2 Representation Theory
Abstract
Broline, Crowe and Isaacs have computed the determinant of a matrix associated to a Conway-Coxeter frieze pattern. We generalise their result to the corresponding frieze pattern of cluster variables arising from the Fomin-Zelevinsky cluster algebra of type A. We give a representation-theoretic interpretation of this result in terms of certain configurations of indecomposable objects in the root category of type A.
Keywords
Cite
@article{arxiv.1008.5329,
title = {Categorification of a frieze pattern determinant},
author = {Karin Baur and Bethany Marsh},
journal= {arXiv preprint arXiv:1008.5329},
year = {2020}
}
Comments
14 pages; 8 figures. Sections 1-3 rewritten, postponing the cluster interpretation until Section 3. Minor corrections