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Cluster algebras associated with open Richardson varieties: an algorithm to compute initial seeds

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arxiv 2201.10292 v1 pith:ISNETXZA submitted 2022-01-25 math.RT math.CO

Etienne Ménard This is my paper · ORCID
classification math.RTmath.CO
keywords seedsalgorithmassociatedclustercomputeinitialopenrichardson
verification ladder T0 review T1 audit T2 compute T3 formal
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We present a new algorithm to compute initial seeds for cluster structures on categories associated with coordinate rings of open Richardson varieties. This allows us to explicitely determine seeds first considered in Leclerc's 2016 article.

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Cited by 2 Pith papers

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  1. Upper cluster structure on Kac--Moody Richardson varieties

    math.RT 2025-06 conditional novelty 7.0 of 10

    Open Richardson varieties in symmetrizable Kac-Moody flag varieties, including twisted-product cases, are shown to carry upper cluster algebra coordinate rings.

  2. Towards Monoidal Categorifications of Twisted Products of Flag Varieties

    math.RT 2026-02 conditional novelty 6.0 of 10

    The Grothendieck ring of the intersection of two monoidal categories C(β)∩C_v contains the cluster algebra of the twisted product of flag varieties, with cluster monomials given by classes of simple objects.

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