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On Leclerc's conjectural cluster structures for open Richardson varieties
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On Leclerc's conjectural cluster structures for open Richardson varieties
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In 2016, Leclerc constructed conjectural cluster structures on open Richardson varieties using representations of preprojective algebras. A variant with more explicit seeds was obtained by M\'enard in his thesis. We show that M\'enard's seeds do yield *upper* cluster algebra structures on open Richardson varieties and discuss the problems that remain in order to prove that they are cluster algebra structures.
Forward citations
Cited by 2 Pith papers
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Frayed Demazure weaves for Poisson-compatible cluster structures on Bott--Samelson charts
Frayed Demazure weaves yield Poisson-compatible cluster structures on Bott-Samelson charts whose transitions are rational quasi-cluster morphisms, with mutation sequences related to Ménard's open Richardson seeds.
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Quantum cluster algebra realization for stated ${\rm SL}_n$-skein algebras and rotation-invariant bases for polygons
For polygonal surfaces, the localized stated SL_n-skein algebra equals the associated quantum cluster algebra, producing a rotation-invariant basis.
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