Crystal Bases for Quantum Generalized Kac-Moody Algebras

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dc.creatorJeong, Kyeonghoon
dc.creatorKang, Seok-Jin
dc.creatorKashiwara, Masaki
dc.date2003-05-28
dc.date.accessioned2026-07-07T04:58:19Z
dc.date.available2026-07-07T04:58:19Z
dc.descriptionIn 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 $U_q^-(\mathfrak g)$.
dc.description60 pages, no figures
dc.identifierhttps://arxiv.org/abs/math/0305390
dc.identifierhttp://arxiv.org/abs/math/0305390
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67592
dc.subjectQuantum Algebra
dc.subject17B37
dc.titleCrystal Bases for Quantum Generalized Kac-Moody Algebras
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