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Crystals from categorified quantum groups

Abstract : 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.
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Aaron D. Lauda, Monica Vazirani. Crystals from categorified quantum groups. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 2010, San Francisco, United States. pp.869-880. ⟨hal-01186267⟩

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