Leclerc's conjecture on a cluster structure for type A Richardson varieties

Khrystyna Serhiyenko, Melissa Sherman-Bennett

Research output: Contribution to journalArticlepeer-review

Abstract

Leclerc [32] constructed a conjectural cluster structure on Richardson varieties in simply laced types using cluster categories. We show that in type A, his conjectural cluster structure is in fact a cluster structure. We do this by comparing Leclerc's construction with another cluster structure on type A Richardson varieties due to Ingermanson [27]. Ingermanson's construction uses the combinatorics of wiring diagrams and the Deodhar stratification. Though the two cluster structures are defined very differently, we show that the quivers coincide and clusters are related by the twist map for Richardson varieties, recently defined by Galashin–Lam [21].

Original languageEnglish
Article number109698
JournalAdvances in Mathematics
Volume447
DOIs
StatePublished - Jun 2024

Bibliographical note

Publisher Copyright:
© 2024 Elsevier Inc.

Keywords

  • Cluster algebra
  • Preprojective algebra
  • Richardson variety

ASJC Scopus subject areas

  • General Mathematics

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