• Journal of the Korean Mathematical Society
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• v.45 no.4
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• pp.1135-1202
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• 2008

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 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.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1123-1128
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• 1996

Let A be an (nonassociative) algebra with multiplication xy over a field F, and denote by $A^-$ the algebra with multiplication [x, y] = xy - yx$ defined on the vector space A. If $A^-$ is a Lie algebra, then A is called Lie-admissible. Lie-admissible algebras arise in various topics, including geometry of invariant affine connections on Lie groups and classical and quantum mechanics(see [2, 5, 6, 7] and references therein).