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http://dx.doi.org/10.4134/JKMS.2008.45.4.1135

FOCK SPACE REPRESENTATIONS OF QUANTUM AFFINE ALGEBRAS AND GENERALIZED LASCOUX-LECLERC-THIBON ALGORITHM  

Kang, Seok-Jin (Department of Mathematical Sciences Seoul National University)
Kwon, Jae-Hoon (Department of Mathematics University of Seoul)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.4, 2008 , pp. 1135-1202 More about this Journal
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 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;
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