Coordinate rings of many varieties naturally occurring in representation theory are known to admit a cluster algebra structure. Leclerc constructed a conjectural cluster structure on Richardson varieties using categorification in terms of module categories of the preprojective algebras. We show that in type A, his conjectural cluster structure is in fact a cluster structure. We do this by comparing Leclerc’s construction with another cluster structure due to Ingermanson, which uses the combinatorics of wiring diagrams and the Deodhar stratification.
This is joint work with Melissa Sherman-Bennett.
This video was part of the Maurice Auslander International Conference.
