Cluster structures on strata of flag varieties
Representation Theory
2015-01-06 v3 Rings and Algebras
Abstract
We introduce some new Frobenius subcategories of the module category of a preprojective algebra of Dynkin type, and we show that they have a cluster structure in the sense of Buan-Iyama-Reiten-Scott. These categorical cluster structures yield cluster algebra structures in the coordinate rings of intersections of opposed Schubert cells.
Cite
@article{arxiv.1402.4435,
title = {Cluster structures on strata of flag varieties},
author = {Bernard Leclerc},
journal= {arXiv preprint arXiv:1402.4435},
year = {2015}
}
Comments
31 pages, v.2 : a comment about the relation to Muller-Speyer conjecture on positroid varieties is added in 7.3. v.3. final version, to appear in Advances in Math