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

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

2003-07-07

arxiv.org/abs/math/0307082v2

Mathematics

Representation Theory

27 pages; A brief introduction added, references updated and expanded, the final version to appear in Moscow Mathematical Jour

Scientific paper

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 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.

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