Periodic Staircase Matrices and Generalized Cluster Structures

Misha Gekhtman; Michael Shapiro; Alek Vainshtein

doi:10.1093/imrn/rnaa148

Periodic Staircase Matrices and Generalized Cluster Structures

Misha Gekhtman, Michael Shapiro, Alek Vainshtein

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	4181-4221
Number of pages	41
Journal	International Mathematics Research Notices
Volume	2022
Issue number	6
DOIs	https://doi.org/10.1093/imrn/rnaa148
State	Published - 1 Mar 2022

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© 2020 The Author(s) 2020. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: [email protected].

ASJC Scopus subject areas

General Mathematics

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10.1093/imrn/rnaa148

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N2 - 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.

AB - 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.

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M3 - Article

AN - SCOPUS:85127173854

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JO - International Mathematics Research Notices

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Periodic Staircase Matrices and Generalized Cluster Structures

Abstract

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