Dans ce travail, nous étudions certaines sous-catégories monoïdales (introduites par David Hernandez et Bernard Leclerc) de représentations de dimension finie d’une algèbre affine de type . Nous classifions l’ensemble des représentations premières de ces sous-catégories, et donnons des conditions nécessaires et suffisantes pour que le produit tensoriel des deux représentations premières soit irréductible. Dans le cas où le produit tensoriel est réductible, nous décrivons une factorisation en modules premiers des facteurs simples. En conséquence, nous prouvons que ces sous-catégories monoïdales sont des catégorifications monoïdales d’algèbres amassées de type avec coefficients.
We study certain monoidal subcategories (introduced by David Hernandez and Bernard Leclerc) of finite-dimensional representations of a quantum affine algebra of type . 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 with coefficients.
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@article{JEP_2019__6__581_0,
author = {Matheus Brito and Vyjayanthi Chari},
title = {Tensor products and $q$-characters of {HL-modules} and monoidal categorifications},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {581--619},
publisher = {\'Ecole polytechnique},
volume = {6},
year = {2019},
doi = {10.5802/jep.101},
zbl = {07114034},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.101/}
}
TY - JOUR AU - Matheus Brito AU - Vyjayanthi Chari TI - Tensor products and $q$-characters of HL-modules and monoidal categorifications JO - Journal de l’École polytechnique — Mathématiques PY - 2019 SP - 581 EP - 619 VL - 6 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.101/ DO - 10.5802/jep.101 LA - en ID - JEP_2019__6__581_0 ER -
%0 Journal Article %A Matheus Brito %A Vyjayanthi Chari %T Tensor products and $q$-characters of HL-modules and monoidal categorifications %J Journal de l’École polytechnique — Mathématiques %D 2019 %P 581-619 %V 6 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.101/ %R 10.5802/jep.101 %G en %F JEP_2019__6__581_0
Matheus Brito; Vyjayanthi Chari. Tensor products and $q$-characters of HL-modules and monoidal categorifications. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 581-619. doi : 10.5802/jep.101. https://jep.centre-mersenne.org/articles/10.5802/jep.101/
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