Monoidal categorification on some open Richardson varieties

Abstract

In this paper, we investigate the cluster morphisms between cluster algebras and the functor of monoidal categories. Our findings demonstrate that there exists a monoidal categorification of the coordinate ring of the open Richardson variety $\mathcal{R}_{w,v}$, where $w=vu$ and $\ell(w)=\ell(u)+\ell(v)$. This result confirms a conjecture proposed by Kashiwara, Kim, Oh, and Park.