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arXiv:2309.13867 [math.RT]AbstractReferencesReviewsResources

Cellularity of KLR and weighted KLRW algebras via crystals

Andrew Mathas, Daniel Tubbenhauer

Published 2023-09-25Version 1

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 compute the graded decomposition numbers of the cyclotomic algebras.

Comments: 48 pages, many figures, comments welcome
Categories: math.RT, math.CO, math.RA
Subjects: 18M30, 20C08, 05E10, 17B10, 18N25
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