Computing fusion products of MV cycles using the Mirković–Vybornov isomorphism

Journal of Combinatorial Algebra

article

Roger Bai¹  Anne Dranowski²  Joel Kamnitzer¹ 

[1] University of Toronto;University of Southern California

关键词: Cluster algebras;    affine Grassmannians;    perfect bases;    rank varieties;    fusion;   

DOI  :  10.4171/jca/69

学科分类：外科医学

来源: European Mathematical Society

【 摘 要 】

The fusion of two Mirković–Vilonen cycles is a degeneration of their product, defined using the Beilinson–Drinfeld Grassmannian. In this paper, we put in place a conceptually elementary approach to computing this product in type AAA. We do so by transferring the problem to a fusion of generalized orbital varieties using the Mirković–Vybornov isomorphism. As an application, we explicitly compute all cluster exchange relations in the coordinate ring of the upper-triangular subgroup of GL4\mathbf{GL}_4GL4​, confirming that all the cluster variables are contained in the Mirković–Vilonen basis.

【 授权许可】

CC BY