Computing fusion products of MV cycles using the Mirković–Vybornov isomorphism
Roger Bai
University of Toronto, CanadaAnne Dranowski
University of Southern California, Los Angeles, USAJoel Kamnitzer
University of Toronto, Canada
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Abstract
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 . 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 , confirming that all the cluster variables are contained in the Mirković–Vilonen basis.
Cite this article
Roger Bai, Anne Dranowski, Joel Kamnitzer, Computing fusion products of MV cycles using the Mirković–Vybornov isomorphism. J. Comb. Algebra 7 (2023), no. 1/2, pp. 83–126
DOI 10.4171/JCA/69