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arXiv · 2004.12466

An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras

Fan Qin
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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.

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BibTeXRIS

Fan Qin. 2020-04-26. An Analog of Leclerc's Conjecture for Bases of Quantum Cluster Algebras. https://doi.org/10.3842/sigma.2020.122

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