Crystal Bases for Quantum Generalized Kac-Moody Algebras |
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| Authors: | Jeong, Kyeonghoon Kang, Seok-Jin Kashiwara, Masaki |
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| Affiliation: | Department of Mathematics, NS30, Seoul National University Seoul 151-747, South Korea. E-mail: khjeong{at}math.snu.ac.kr, sjkang{at}kias.re.kr
Research Institute for Mathematical Sciences, Kyoto University Kyoto 606, Japan. E-mail: masaki{at}kurims.kyoto-u.ac.jp |
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| Abstract: | In this paper, we develop the crystal basis theory for quantumgeneralized KacMoody algebras. For a quantum generalizedKacMoody algebra Uq(g), we first introduce the categoryOint of Uq(g)-modules and prove its semisimplicity. Next, wedefine the notion of crystal bases for Uq(g)-modules in thecategory Oint and for the subalgebra  . We then prove the tensor product rule and the existence theoremfor crystal bases. Finally, we construct the global bases forUq(g)-modules in the category Oint and for the subalgebra . 2000 Mathematics Subject Classification17B37, 17B67. |
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| Keywords: | generalized Kac– Moody algebra crystal base global base |
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