Categorification of a frieze pattern determinant

Details Categorification of a frieze pattern determinant Categorification of a frieze pattern determinant

2010-08-31

arxiv.org/abs/1008.5329v1

Mathematics

Combinatorics

12 pages; 7 figures

Scientific paper

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.

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