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This article is cited in 5 scientific papers (total in 5 papers)
Categorification of highest weight modules over quantum generalized Kac–Moody algebras
Seok-Jin Kanga, Masaki Kashiwarabc, Se-Jin Ohd a Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-747, Korea
b Department of Mathematical Sciences, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-747, Korea
c Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
d Pohang Mathematics Institute, Pohang University of Science and Technology, San31 Hyoja-Dong Nam-Gu, Pohang 790-784, Korea
Abstract:
Let $U_q(\mathfrak g)$ be a quantum generalized Kac–Moody algebra and let $V(\Lambda)$ be the integrable highest weight $U_q(\mathfrak g)$-module with highest weight $\Lambda$. We prove that the cyclotomic Khovanov–Lauda–Rouquier algebra $R^\Lambda$ provides a categorification of $V(\Lambda)$.
Key words and phrases:
categorification, Khovanov–Lauda–Rouquier algebras, cyclotomic quotient, quantum generalized Kac–Moody algebras.
Received: June 14, 2011; in revised form March 17, 2012
Citation:
Seok-Jin Kang, Masaki Kashiwara, Se-Jin Oh, “Categorification of highest weight modules over quantum generalized Kac–Moody algebras”, Mosc. Math. J., 13:2 (2013), 315–343
Linking options:
https://www.mathnet.ru/eng/mmj499 https://www.mathnet.ru/eng/mmj/v13/i2/p315
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