English

On Leclerc's conjectural cluster structures for open Richardson varieties

Representation Theory 2022-07-22 v1

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.

Keywords

Cite

@article{arxiv.2207.10184,
  title  = {On Leclerc's conjectural cluster structures for open Richardson varieties},
  author = {Peigen Cao and Bernhard Keller},
  journal= {arXiv preprint arXiv:2207.10184},
  year   = {2022}
}

Comments

11 pages

R2 v1 2026-06-25T01:05:52.529Z