Categorification of a frieze pattern determinant
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2010
- DOI:
- 10.48550/arXiv.1008.5329
- arXiv:
- arXiv:1008.5329
- Bibcode:
- 2010arXiv1008.5329B
- Keywords:
-
- Mathematics - Combinatorics;
- Mathematics - Representation Theory;
- 05B30 (Primary) 16G20;
- 18E30;
- 05E15 (Secondary) 13F60;
- 16G70;
- 52C99
- E-Print:
- 14 pages