Periodic staircase matrices and generalized cluster structures

Abstract

As is well-known, cluster transformations in cluster structures of geometric type are often modeled on determinant identities, such as short Plucker 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.

30 pages, 6 figures

References in corpus (1)

• Plethora of cluster structures on $G{L}_n$

Cited by in corpus (3)

• Cyclic symmetry loci in Grasssmannians
• Multiple generalized cluster structures on $D({\text{GL}}_n)$
• Generalized Cluster Structures Related to the Drinfeld Double of $G{L}_n$