Cluster structures on strata of flag varieties

By Bernard Leclerc. 2014

69 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8500bf3e835e26ab9bd8f5ad8d8b988e1f643217

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Positive geometries and canonical forms (2017, background): “We remark that it is strongly expected that Π̊u (and in particular the open stratum inside G/P ) is a cluster variety [20].”
Positroid varieties and cluster algebras (2019, methodology): “In particular, following ideas of [SSBW19], we show in Section 2 that the cluster algebra of [Lec16] is isomorphic to A(QD) (i.”
Cluster Algebras of Grassmannians are Locally Acyclic (2014, background): “This includes some double Bruhat cells; in the case of GL e,(14) 4 , the target-labeling convention gives the cluster structure from [BFZ05], while the source-labeling convention gives the image of this cluster structure under the adjugate map.5 This mirror image cluster algebra appears to be closer”
The twist for positroid varieties (2016, background): “Leclerc [18] has recently placed a cluster structure on Π̃◦(M), which we expect to coincide with this one, but the details are not yet checked.”