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arXiv:1402.4435 [math.RT]AbstractReferencesReviewsResources

Cluster structures on strata of flag varieties

Bernard Leclerc

Published 2014-02-18, updated 2015-01-05Version 3

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.

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
Categories: math.RT, math.RA
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