11 citations · 47 across the 7 of their papers we have counts for
9 papers · 1 filter
Cluster algebras: notes for 2004 IMCC (Chonju, Korea, August 2004)
Andrei Zelevinsky
This is an expanded version of the notes for the two lectures at the 2004 International Mathematics Conference (Chonbuk National University, August 4-6, 2004). The first lecture di…
Cluster algebras: Notes for the CDM-03 conference
Sergey Fomin, Andrei Zelevinsky
This is an expanded version of the notes of our lectures given at the conference "Current Developments in Mathematics 2003" held at Harvard University on November 21--22, 2003. We…
Positivity and canonical bases in rank 2 cluster algebras of finite and affine types
Paul Sherman, Andrei Zelevinsky
The main motivation for the study of cluster algebras initiated in math.RT/0104151, math.RA/0208229 and math.RT/0305434 was to design an algebraic framework for understanding total…
Cluster algebras III: Upper bounds and double Bruhat cells
Arkady Berenstein, Sergey Fomin, Andrei Zelevinsky
We continue the study of cluster algebras initiated in math.RT/0104151 and math.RA/0208229. We develop a new approach based on the notion of an upper cluster algebra, defined as an…
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…
Cluster algebras I: Foundations
Sergey Fomin, Andrei Zelevinsky
In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.