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Cluster Monomials are Dual Canonical

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arxiv 2112.04109 v1 pith:RY2NS7TR submitted 2021-12-08 math.QA math.RT

Peter J. McNamara This is my paper · ORCID
classification math.QAmath.RT
keywords clustercanonicaldualmonomialsalgebraalgebrasassumptionbasis
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Kang, Kashiwara, Kim and Oh have proved that cluster monomials lie in the dual canonical basis, under a symmetric type assumption. This involves constructing a monoidal categorification of a quantum cluster algebra using representations of KLR algebras. We use a folding technique to generalise their results to all Lie types.

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  1. Affine highest weight structures on module categories over quiver Hecke algebras

    math.RT 2024-12 conditional novelty 7.0 of 10

    Quiver Hecke algebra module categories of arbitrary symmetrizable type admit Kleshchev stratifications, and quantum-unipotent subcategories are affine highest weight categories.

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