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

권재훈|강석진
대한수학회 (The Korean Mathematical Society)|2008.07|대한수학회지 (Journal of the KMS)|제45권 제4호|pp. 1135-1202

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참고문헌

키워드

quantum affine algebracrystal basisglobal basis
주제분류수학

초록

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.

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.

참고문헌 (19)

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