Computing fusion products of MV cycles using the Mirkovi\'c--Vybornov isomorphism

IF 0.6 2区 数学 Q3 MATHEMATICS
R. Bai, Anne Dranowski, J. Kamnitzer
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引用次数: 1

Abstract

The fusion of two Mirkovic-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 $A$. We do so by transferring the problem to a fusion of generalized orbital varieties using the Mirkovic-Vybornov isomorphism. As an application, we explicitly compute all cluster exchange relations in the coordinate ring of the upper-triangular subgroup of $GL_4$, confirming that all the cluster variables are contained in the Mirkovic-Vilonen basis.
利用Mirkovi\ c—Vybornov同构计算MV循环的聚变积
两个Mirkovic-Vilonen循环的融合是它们乘积的退化,使用Beilinson-Drinfeld Grassmannian来定义。在本文中,我们提出了一种概念上基本的方法来计算类型为$ a $的这个乘积。我们通过使用Mirkovic-Vybornov同构将问题转化为广义轨道变体的融合来做到这一点。作为应用,我们显式计算了$GL_4$上三角子群的坐标环上的所有簇交换关系,确认了所有簇变量都包含在Mirkovic-Vilonen基中。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.20
自引率
0.00%
发文量
9
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