Andrei Zelevinsky, Northeastern University
Cluster algebras of finite type via principal minors

This is a joint work with Shih-Wei Yang. We give a unified geometric realization for the cluster algebra of an arbitrary finite type having principal coefficients at some acyclic cluster (all this terminology will be explained). The cluster algebra in question is realized as the coordinate ring of a certain double Bruhat cell in the complex semisimple algebraic group of the same Cartan-Killing type. In this realization the set of cluster variables is some explicitly determined collection of (generalized) principal minors.

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