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Cellularity of KLR and weighted KLRW algebras via crystals

· 2023 · math.RT · arXiv 2309.13867

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abstract

We prove that the weighted KLRW algebras of finite type, and their cyclotomic quotients, are cellular algebras. The cellular bases are explicitly described using crystal graphs. As a special case, this proves that the KLR algebras of finite type are cellular. As one application, we give explicit formulas for the graded decomposition numbers of the cyclotomic algebras in level one.

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math.RT 1

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2026 1

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Presentations for categories of crystals

math.RT · 2026-06-01 · unverdicted · novelty 5.0

Provides generators and relations for monoidal crystal categories of simple complex Lie algebras with explicit small-rank examples.

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  • Presentations for categories of crystals math.RT · 2026-06-01 · unverdicted · none · ref 24 · internal anchor

    Provides generators and relations for monoidal crystal categories of simple complex Lie algebras with explicit small-rank examples.