Cluster algebras associated with open Richardson varieties: an algorithm to compute initial seeds

TL;DR

This paper introduces an algorithm to compute initial seeds for cluster structures on categories linked to coordinate rings of open Richardson varieties, enabling explicit seed determination as previously considered by Leclerc.

Contribution

The paper presents a novel algorithm for explicitly computing initial seeds in cluster structures related to open Richardson varieties.

Findings

Algorithm successfully computes initial seeds for the specified cluster structures.

Explicit seeds align with those previously considered by Leclerc.

Enhances understanding of cluster algebra structures in Richardson varieties.

Abstract

We present a new algorithm to compute initial seeds for cluster structures on categories associated with coordinate rings of open Richardson varieties. This allows us to explicitely determine seeds first considered in Leclerc's 2016 article.