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Crystal bases for quantum generalized Kac-Moody algebras
Cited 42 time in
Web of Science
Cited 43 time in Scopus
- Authors
- Issue Date
- 2005
- Publisher
- Oxford University Press
- Citation
- Proc. London Math. Soc. (3) 90 (2005) 395-438
- Keywords
- generalized Kac–Moody algebra ; crystal base ; global 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
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