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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.

Copyright 2002 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 08 (2002), pp. 35-46
• Publisher Identifier: S 1079-6762(02)00103-8
• 2000 Mathematics Subject Classification. Primary 17B37; Secondary 17B10
• Key words and phrases. Quantized universal enveloping algebra, crystal basis, global basis
• Received by editors December 14, 2001
• September 19, 2002
• Communicated by Efim Zelmanov
• Comments (When Available)

Seok-Jin Kang

School of Mathematics, Korea Institute for Advanced Study, Seoul 130-012, Korea

E-mail address: sjkang@kias.re.kr

Jae-Hoon Kwon

School of Mathematics, Korea Institute for Advanced Study, Seoul 130-012, Korea

E-mail address: jhkwon@kias.re.kr