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arXiv · 0909.1810

Crystals from categorified quantum groups

Aaron D. Lauda·Monica Vazirani
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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. 2011-05-03. Crystals from categorified quantum groups. https://doi.org/10.1016/j.aim.2011.06.009

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