English

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

R2 v1 2026-06-21T16:07:31.877Z