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An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras
Fan Qin School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China
Abstract:
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, Leclerc's conjecture.
Received: May 14, 2020; in final form November 13, 2020; Published online November 27, 2020
Citation:
Fan Qin, “An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras”, SIGMA, 16 (2020), 122, 22 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1659 https://www.mathnet.ru/eng/sigma/v16/p122
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Abstract page: | 46 | Full-text PDF : | 21 | References: | 6 |
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