Tensor products and $q$-characters of HL-modules and monoidal categorifications
Brito, Matheus ; Chari, Vyjayanthi
arXiv, Tome 2019 (2019) no. 0, / Harvested from
We study certain monoidal subcategories (introduced by David Hernandez and Bernard Leclerc) of finite--dimensional representations of a quantum affine algebra of type $A$. We classify the set of prime representations in these subcategories and give necessary and sufficient conditions for a tensor product of two prime representations to be irreducible. In the case of a reducible tensor product we describe the prime decomposition of the simple factors. As a consequence we prove that these subcategories are monoidal categorifications of a cluster algebra of type $A$ with coefficients.
Publié le : 2019-01-21
Classification:  Mathematics - Representation Theory,  Mathematics - Quantum Algebra,  17B37, 20G42, 13F60 
@article{1901.07020,
     author = {Brito, Matheus and Chari, Vyjayanthi},
     title = {Tensor products and $q$-characters of HL-modules and monoidal
  categorifications},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1901.07020}
}

Brito, Matheus; Chari, Vyjayanthi. Tensor products and $q$-characters of HL-modules and monoidal
  categorifications. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1901.07020/