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Positivity and canonical bases in rank 2 cluster algebras of finite and affine types

P. Sherman, A. V. Zelevinskii

Northeastern University

Abstract: The main motivation for the study of cluster algebras initiated in [6], [3], [1] was to design an algebraic framework for understanding total positivity and canonical bases in semisimple algebraic groups. In this paper, we introduce and explicitly construct the canonical basis for a special family of cluster algebras of rank 2.

Key words and phrases: Cluster algebras, affine root systems, Newton polygons.

MSC: Primary 16S99; Secondary 05E15, 22E46

Received: July 9, 2003; in revised form December 14, 2003

Language: English

DOI: 10.17323/1609-4514-2004-4-4-947-974

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