J. Korean Math. Soc. 2008; 45(4): 1135-1202
Printed July 1, 2008
Copyright © The Korean Mathematical Society.
Seok-Jin Kang and Jae-Hoon Kwon
Seoul national university, Seoul national university
We construct the Fock space representations of classical quantum affine algebras using combinatorics of Young walls. We also show that the crystal graphs of the Fock space representations can be realized as the abstract crystal consisting of proper Young walls. Finally, we give a generalized version of Lascoux-Leclerc-Thibon algorithm for computing the global bases of the basic representations of classical quantum affine algebras.
Keywords: quantum affine algebra, crystal basis, global basis
MSC numbers: 17B37
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