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Dual canonical bases and quantum cluster algebras

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arxiv 2003.13674 v3 pith:RNAVV44M submitted 2020-03-30 math.QA math.RT

Fan Qin This is my paper · ORCID
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keywords quantumclustercanonicaldualalgebraalgebrasarisingbases
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Given any quantum cluster algebra arising from a quantum unipotent subgroup of symmetrizable Kac-Moody type, we verify the quantization conjecture in full generality that the quantum cluster monomials are contained in the dual canonical basis after rescaling.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Braid group symmetries on Poisson algebras arising from quantum symmetric pairs

    math.QA 2025-07 conditional novelty 7.0 of 10

    For every finite type quantum symmetric pair, the braid group action and a PBW basis descend to the DCKP-type integral form and, via semiclassical limits, yield Poisson automorphisms and explicit Poisson brackets on t...

  2. Crystals and quantum twist automorphisms

    math.RT 2025-07 conditional novelty 7.0 of 10

    The quantum twist automorphism is computed through PBW and string parametrizations of localized crystals, with explicit minuscule Young diagram rules and a closed periodicity formula in type A.

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