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Discrete Mathematics & Theoretical Computer Science |
We study the crystal structure on categories of graded modules over algebras which categorify the negative half of the quantum Kac-Moody algebra associated to a symmetrizable Cartan data. We identify this crystal with Kashiwara's crystal for the corresponding negative half of the quantum Kac-Moody algebra. As a consequence, we show the simple graded modules for certain cyclotomic quotients carry the structure of highest weight crystals, and hence compute the rank of the corresponding Grothendieck group.
Source : ScholeXplorer
IsRelatedTo ARXIV 1304.7837 Source : ScholeXplorer IsRelatedTo DOI 10.1090/s1088-4165-2014-00453-9 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1304.7837
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