Journal of the
Korean Mathematical Society
JKMS

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J. Korean Math. Soc. 2008; 45(4): 1135-1202

Printed July 1, 2008

Copyright © The Korean Mathematical Society.

Fock space representations of quantum affine algebras and generalized Lascoux-Leclerc-Thibon algorithm

Seok-Jin Kang and Jae-Hoon Kwon

Seoul national university, Seoul national university

Abstract

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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