Monoidal categorification on open Richardson varieties

TL;DR

This paper demonstrates that a specific subcategory of modules over quiver Hecke algebras provides a monoidal categorification of the coordinate ring of open Richardson varieties in Dynkin types, enhancing understanding of their algebraic structure.

Contribution

It establishes a new monoidal categorification framework for open Richardson varieties using subcategories of modules over quiver Hecke algebras, after inverting frozen cluster variables.

Findings

Subcategory _{w,v} of modules categorifies coordinate rings of open Richardson varieties.

The categorification holds for all Dynkin types after inverting frozen variables.

Provides a new algebraic perspective on the structure of Richardson varieties.

Abstract

In this paper, we show that the subcategory $\mathscr{C}_{w,v}$ of modules over quiver Hecke algebras is a monoidal categorification of the coordinate ring of any open Richardson variety of Dynkin types after inverting the frozen cluster variables.