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International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm001, 18 pages, doi:10.1093/imrn/rnm001 published on May 24, 2007
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Copyright © The Author 2007. Published by Oxford University Press.

Abstract Crystals for Quantum Generalized Kac-Moody Algebras

Kyeonghoon Jeong1, Seok-Jin Kang1, Masaki Kashiwara2 and Dong-Uy Shin3,

1 Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, San 56-1 Shinrim-Dong, Kwanak-Ku, Seoul, 151–747, Korea
2 Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa, Sakyo-Ku, Kyoto 606–8502, Japan
3 Department of Mathematics, Chonnam National University, Yongbong-dong, Buk-gu, Kwangju, 500-757, Korea

Correspondence: Correspondence to be sent to: Dong-Uy Shin, Department of Mathematics, Chonnam National University, Yongbong-dong, Buk-gu, Kwangju, 500-757, Korea. e-mail: dushin{at}chonnam.ac.kr

In this article, we introduce the notion of abstract crystals for quantum generalized Kac-Moody algebras and study their fundamental properties. We then prove the crystal embedding theorem and give a characterization of the crystals B({infty}) and B({lambda}).

Communicated by Michio Jimbo


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