Cluster structures in mixed Grassmanianns

TL;DR

This paper constructs and explores new cluster structures in the coordinate ring of mixed Grassmannians, generalizing previous results and utilizing the machinery of weaves for analysis.

Contribution

It introduces a family of natural cluster structures in mixed Grassmannians, extending prior work and applying the weaves framework for their study.

Findings

Constructed new cluster structures in mixed Grassmannians.

Connected cluster structures with the machinery of weaves.

Generalized previous results by Fomin-Pylyavskyy and Carde.

Abstract

Generalizing the results by Fomin-Pylyavskyy and Carde, we construct a family of natural cluster structures in the coordinate ring of a mixed Grassmannian, the configuration space of tuples of several vectors and covectors in a finite-dimensional complex vector space. We describe and explore these cluster structures using the machinery of weaves introduced by Casals and Zaslow.