Geodesic
Prime representations in the Hernandez–Leclerc category: classical decompositions
Canadian journal of mathematics, Tome 76 (2024) no. 6, pp. 1987-2018

Voir la notice de l'article provenant de la source Cambridge

DOI

We use the dual functional realization of loop algebras to study the prime irreducible objects in the Hernandez–Leclerc (HL) category for the quantum affine algebra associated with $\mathfrak {sl}_{n+1}$. When the HL category is realized as a monoidal categorification of a cluster algebra (Hernandez and Leclerc (2010, Duke Mathematical Journal 154, 265–341); Hernandez and Leclerc (2013, Symmetries, integrable systems and representations, 175–193)), these representations correspond precisely to the cluster variables and the frozen variables are minimal affinizations. For any height function, we determine the classical decomposition of these representations with respect to the Hopf subalgebra $\mathbf {U}_q(\mathfrak {sl}_{n+1})$ and describe the graded multiplicities of their graded limits in terms of lattice points of convex polytopes. Combined with Brito, Chari, and Moura (2018, Journal of the Institute of Mathematics of Jussieu 17, 75–105), we obtain the graded decomposition of stable prime Demazure modules in level two integrable highest weight representations of the corresponding affine Lie algebra.
DOI : 10.4153/S0008414X23000706
Mots-clés : Quantum affine algebras, truncated representations, convex polytopes 
Barth, Leon; Kus, Deniz. Prime representations in the Hernandez–Leclerc category: classical decompositions. Canadian journal of mathematics, Tome 76 (2024) no. 6, pp. 1987-2018. doi: 10.4153/S0008414X23000706
@article{10_4153_S0008414X23000706,
     author = {Barth, Leon and Kus, Deniz},
     title = {Prime representations in the {Hernandez{\textendash}Leclerc} category: classical decompositions},
     journal = {Canadian journal of mathematics},
     pages = {1987--2018},
     year = {2024},
     volume = {76},
     number = {6},
     doi = {10.4153/S0008414X23000706},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000706/}
}
TY  - JOUR
AU  - Barth, Leon
AU  - Kus, Deniz
TI  - Prime representations in the Hernandez–Leclerc category: classical decompositions
JO  - Canadian journal of mathematics
PY  - 2024
SP  - 1987
EP  - 2018
VL  - 76
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000706/
DO  - 10.4153/S0008414X23000706
ID  - 10_4153_S0008414X23000706
ER  - 
%0 Journal Article
%A Barth, Leon
%A Kus, Deniz
%T Prime representations in the Hernandez–Leclerc category: classical decompositions
%J Canadian journal of mathematics
%D 2024
%P 1987-2018
%V 76
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000706/
%R 10.4153/S0008414X23000706
%F 10_4153_S0008414X23000706

Cité par Sources :