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Crystal bases for quantum generalized Kac-Moody algebras

Cited 37 time in Web of Science Cited 37 time in Scopus
Authors
Kang, Seok-Jin; Jeong, Kyeonghoon; Kashiwara, Masaki
Issue Date
2005
Publisher
Oxford University Press
Citation
Proc. London Math. Soc. (3) 90 (2005) 395-438
Keywords
generalized Kac–Moody algebracrystal baseglobal base
Abstract
In this paper, we develop the crystal basis theory for quantum generalized Kac–Moody algebras. For a quantum generalized Kac–Moody algebra $U_q(\mathfrak{g})$, we first introduce the category $\mathcal{O}_{int}$ of $U_q(\mathfrak{g})$-modules and prove its semisimplicity. Next, we define the notion of crystal bases for $U_q(\mathfrak{g})$-modules in the category $\mathcal{O}_{int}$ and for the subalgebra $U_q^-(\mathfrak{g})$. We then prove the tensor product rule and the existence theorem for crystal bases. Finally, we construct the global bases for $U_q(\mathfrak{g})$-modules in the category $\mathcal{O}_{int}$ and for the subalgebra $U_q^-(\mathfrak{g})$.
ISSN
0024-6115
Language
English
URI
http://hdl.handle.net/10371/12158
DOI
https://doi.org/10.1112/S0024611504015023
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)