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ISSN 1079-6762

 

Quantum affine algebras, combinatorics of Young walls, and global bases


Authors: Seok-Jin Kang and Jae-Hoon Kwon
Journal: Electron. Res. Announc. Amer. Math. Soc. 8 (2002), 35-46
MSC (2000): Primary 17B37; Secondary 17B10
Published electronically: September 19, 2002
MathSciNet review: 1928500
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Abstract: We construct the Fock space representation of quantum affine algebras using combinatorics of Young walls. We also show that the crystal basis of the Fock space representation can be realized as the abstract crystal consisting of proper Young walls. We then generalize Lascoux-Leclerc-Thibon algorithm to obtain an effective algorithm for constructing the global bases of basic representations.


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Additional Information

Seok-Jin Kang
Affiliation: School of Mathematics, Korea Institute for Advanced Study, Seoul 130-012, Korea
Email: sjkang@kias.re.kr

Jae-Hoon Kwon
Affiliation: School of Mathematics, Korea Institute for Advanced Study, Seoul 130-012, Korea
Email: jhkwon@kias.re.kr

DOI: http://dx.doi.org/10.1090/S1079-6762-02-00103-8
PII: S 1079-6762(02)00103-8
Keywords: Quantized universal enveloping algebra, crystal basis, global basis
Received by editor(s): December 14, 2001
Published electronically: September 19, 2002
Communicated by: Efim Zelmanov
Article copyright: © Copyright 2002 American Mathematical Society



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