Aaron D. Lauda ; Monica Vazirani - Crystals from categorified quantum groups

dmtcs:2839 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010) - https://doi.org/10.46298/dmtcs.2839
Crystals from categorified quantum groupsArticle

Authors: Aaron D. Lauda ORCID1; Monica Vazirani 2

  • 1 Department of Mathematics [Vancouver]
  • 2 Department of Mathematics [Univ California Davis]

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.

https://doi.org/10.46298/dmtcs.2839
Source: HAL:hal-01186267v1
Volume: DMTCS Proceedings vol. AN, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010)
Section: Proceedings
Published on: January 1, 2010
Imported on: January 31, 2017
Keywords: Khovanov-Lauda-Rouquier algebras,quiver Hecke algebras,categorification,[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Categorification of Quantum Groups; Funder: National Science Foundation; Code: 0855713
  • EMSW21-RTG: New Techniques in Low-Dimensional Topology and Geometry; Funder: National Science Foundation; Code: 0739392

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