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arXiv · 2009.09461

Hernandez-Leclerc modules and snake graphs

Bing Duan·Jian-Rong Li·Yan-Feng Luo
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Abstract

In 2010, Hernandez and Leclerc studied connections between representations of quantum affine algebras and cluster algebras. In 2019, Brito and Chari defined a family of modules over quantum affine algebras, called Hernandez-Leclerc modules. We characterize the highest $\ell$-weight monomials of Hernandez-Leclerc modules. We give a non-recursive formula for $q$-characters of Hernandez-Leclerc modules using snake graphs, which involves an explicit formula for $F$-polynomials. We also give a new recursive formula for $q$-characters of Hernandez-Leclerc modules.

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Bing Duan, Jian-Rong Li, Yan-Feng Luo. 2020-09-20. Hernandez-Leclerc modules and snake graphs. https://arxiv.org/abs/2009.09461

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