Cluster algebras and quantum affine algebras

Cluster algebras and quantum affine algebras

David Hernandez and Bernard Leclerc

Source: Duke Math. J. Volume 154, Number 2 (2010), 265-341.

Abstract

Let ${\mathcal C}$ be the category of finite-dimensional representations of a quantum affine algebra $U_q(\widehat{\mathfrak g})$ of simply laced type. We introduce certain monoidal subcategories ${\mathcal C}_\ell (\ell\in{\mathbb N})$ of ${\mathcal C}$, and we study their Grothendieck rings using cluster algebras.

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Primary Subjects: 17B37

Secondary Subjects: 16D90

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1281963651
Digital Object Identifier: doi:10.1215/00127094-2010-040
Zentralblatt MATH identifier: 05788166
Mathematical Reviews number (MathSciNet): MR2682185

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