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arXiv · 2207.10184

On Leclerc's conjectural cluster structures for open Richardson varieties

Peigen Cao·Bernhard Keller
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Abstract

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.

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Peigen Cao, Bernhard Keller. 2022-07-20. On Leclerc's conjectural cluster structures for open Richardson varieties. https://arxiv.org/abs/2207.10184

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