Periodic Staircase Matrices and Generalized Cluster Structures

Misha Gekhtman, Michael Shapiro, Alek Vainshtein

Research output: Contribution to journalArticlepeer-review


As is well known, cluster transformations in cluster structures of geometric type are often modeled on determinant identities, such as short Plücker relations, Desnanot-Jacobi identities, and their generalizations. We present a construction that plays a similar role in a description of generalized cluster transformations and discuss its applications to generalized cluster structures in $GL n$ compatible with a certain subclass of Belavin-Drinfeld Poisson-Lie brackets, in the Drinfeld double of $GL n$, and in spaces of periodic difference operators.

Original languageEnglish
Pages (from-to)4181-4221
Number of pages41
JournalInternational Mathematics Research Notices
Issue number6
StatePublished - 1 Mar 2022

Bibliographical note

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ASJC Scopus subject areas

  • General Mathematics


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