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An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras
Symmetry, integrability and geometry: methods and applications, Tome 16 (2020) Cet article a éte moissonné depuis la source Math-Net.Ru

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Dual canonical bases are expected to satisfy a certain (double) triangularity property by Leclerc's conjecture. We propose an analogous conjecture for common triangular bases of quantum cluster algebras. We show that a weaker form of the analogous conjecture is true. Our result applies to the dual canonical bases of quantum unipotent subgroups. It also applies to the $t$-analogs of $q$-characters of simple modules of quantum affine algebras.
Keywords: dual canonical bases, cluster algebras
Mots-clés : Leclerc's conjecture. 
@article{SIGMA_2020_16_a121,
     author = {Fan Qin},
     title = {An {Analog} of {Leclerc's} {Conjecture} for {Bases} of {Quantum} {Cluster} {Algebras}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2020},
     volume = {16},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a121/}
}
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Fan Qin. An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras. Symmetry, integrability and geometry: methods and applications, Tome 16 (2020). http://geodesic.mathdoc.fr/item/SIGMA_2020_16_a121/

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