559 citations · 1k across the 44 of their papers we have counts for
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Cluster algebras II: Finite type classification
Sergey Fomin, Andrei Zelevinsky
This paper continues the study of cluster algebras initiated in math.RT/0104151. Its main result is the complete classification of the cluster algebras of finite type, i.e., those…
Generalized associahedra via quiver representations
Bethany Marsh, Markus Reineke, Andrei Zelevinsky
We provide a quiver-theoretic interpretation of certain smooth complete simplicial fans associated to arbitrary finite root systems in recent work of S. Fomin and A. Zelevinsky. Th…
On symplectic leaves and integrable systems in standard complex semisimple Poisson-Lie groups
Mikhail Kogan, Andrei Zelevinsky
We provide an explicit description of symplectic leaves of a simply connected connected semisimple complex Lie group equipped with the standard Poisson-Lie structure. This sharpens…
Polytopal realizations of generalized associahedra
Frederic Chapoton, Sergey Fomin, Andrei Zelevinsky
In hep-th/0111053, a complete simplicial fan was associated to an arbitrary finite root system. It was conjectured that this fan is the normal fan of a simple convex polytope (a ge…
From Littlewood-Richardson coefficients to cluster algebras in three lectures
Andrei Zelevinsky
This is an expanded version of the notes of my three lectures at a NATO Advanced Study Institute ``Symmetric functions 2001: surveys of developments and perspectives" (Isaac Newton…