Computing fusion products of MV cycles using the Mirkovi\'c--Vybornov isomorphism
نویسندگان
چکیده
The fusion of two Mirkovic-Vilonen cycles is a degeneration their product, defined using the Beilinson-Drinfeld Grassmannian. In this paper, we put in place conceptually elementary approach to computing product type $A$. We do so by transferring problem generalized orbital varieties Mirkovic-Vybornov isomorphism. As an application, explicitly compute all cluster exchange relations coordinate ring upper-triangular subgroup $GL_4$, confirming that variables are contained basis.
منابع مشابه
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We study, in type A, the algebraic cycles (MV-cycles) discovered by I. Mirkovi´c and K. Vilonen [MV]. In particular, we partition the loop Grassmannian into smooth pieces such that the MV-cycles are their closures. We explicitly describe the points in each piece using the lattice model of the loop Grassmannian in type A. The partition is invariant under the action of the coweights and, up to th...
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ژورنال
عنوان ژورنال: Journal of combinatorial algebra
سال: 2023
ISSN: ['2415-6302', '2415-6310']
DOI: https://doi.org/10.4171/jca/69