Positroid varieties and cluster algebras
Pavel Galashin, Thomas Lam
TL;DR
This paper proves that the coordinate rings of open positroid varieties are exactly the cluster algebras derived from Postnikov diagrams, confirming several conjectures and extending previous results in the field.
Contribution
It establishes a precise correspondence between positroid varieties and cluster algebras, confirming longstanding conjectures and generalizing earlier findings.
Findings
Coordinate ring of open positroid varieties equals cluster algebra from Postnikov diagrams
Confirmed conjectures of Postnikov, Muller--Speyer, and Leclerc
Extended results of Scott and Serhiyenko et al.
Abstract
We show that the coordinate ring of an open positroid variety coincides with the cluster algebra associated to a Postnikov diagram. This confirms conjectures of Postnikov, Muller--Speyer, and Leclerc, and generalizes results of Scott and Serhiyenko--Sherman-Bennett--Williams.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory