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Crystal bases for quantum generalized Kac-Moody algebras
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Kang, Seok-Jin | - |
dc.contributor.author | Jeong, Kyeonghoon | - |
dc.contributor.author | Kashiwara, Masaki | - |
dc.date.accessioned | 2009-11-15T23:35:39Z | - |
dc.date.available | 2009-11-15T23:35:39Z | - |
dc.date.issued | 2005 | - |
dc.identifier.citation | Proc. London Math. Soc. (3) 90 (2005) 395-438 | en |
dc.identifier.issn | 0024-6115 | - |
dc.identifier.uri | https://hdl.handle.net/10371/12158 | - |
dc.description.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 $U_q^-(\mathfrak{g})$. | en |
dc.description.sponsorship | The research of Seok-Jin Kang was supported by KOSEF Grant #R01-2003-000-10012-0 and KRF Grant #2003-070-C00001. | en |
dc.language.iso | en | - |
dc.publisher | Oxford University Press | en |
dc.subject | generalized Kac–Moody algebra | en |
dc.subject | crystal base | en |
dc.subject | global base | en |
dc.title | Crystal bases for quantum generalized Kac-Moody algebras | en |
dc.type | Article | en |
dc.contributor.AlternativeAuthor | 강석진 | - |
dc.contributor.AlternativeAuthor | 정경훈 | - |
dc.identifier.doi | 10.1112/S0024611504015023 | - |
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