Hernandez-Leclerc modules and snake graphs

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.

arXiv comment36 pages, latex, minor corrections, complements

References in corpus (6)

• Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras
• The q-characters of representations of quantum affine algebras and deformations of W-algebras
• Cluster algebras and continued fractions
• Categorification of skew-symmetrizable cluster algebras
• Path description of type B q-characters
• A geometric $q$-character formula for snake modules