## Duke Mathematical Journal

### Cluster algebras and quantum affine algebras

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 16 August 2010

https://projecteuclid.org/euclid.dmj/1281963651

Digital Object Identifier
doi:10.1215/00127094-2010-040

Mathematical Reviews number (MathSciNet)
MR2682185

Zentralblatt MATH identifier
1284.17010

#### Citation

Hernandez, David; Leclerc, Bernard. Cluster algebras and quantum affine algebras. Duke Math. J. 154 (2010), no. 2, 265--341. doi:10.1215/00127094-2010-040. https://projecteuclid.org/euclid.dmj/1281963651

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