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

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

2002-08-27

arxiv.org/abs/math/0208204v1

Mathematics

Quantum Algebra

70 pages

Scientific paper

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.

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