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FOCK SPACE REPRESENTATIONS OF QUANTUM AFFINE ALGEBRAS AND GENERALIZED LASCOUX-LECLERC-THIBON ALGORITHM
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 Title & Authors
FOCK SPACE REPRESENTATIONS OF QUANTUM AFFINE ALGEBRAS AND GENERALIZED LASCOUX-LECLERC-THIBON ALGORITHM
Kang, Seok-Jin; Kwon, Jae-Hoon;
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 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;
 Language
English
 Cited by
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Representation type of finite quiver Hecke algebras of type, Journal of Algebra, 2014, 397, 457  crossref(new windwow)
2.
Crystal bases for quantum affine algebras and Young walls, Journal of Algebra, 2009, 322, 6, 1979  crossref(new windwow)
3.
Young walls and graded dimension formulas for finite quiver Hecke algebras of type $$A^{(2)}_{2\ell }$$ A 2 ℓ ( 2 ) and $$D^{(2)}_{\ell +1}$$ D ℓ + 1 ( 2 ), Journal of Algebraic Combinatorics, 2014, 40, 4, 1077  crossref(new windwow)
4.
The Andrews–Olsson identity and Bessenrodt insertion algorithm on Young walls, European Journal of Combinatorics, 2015, 43, 8  crossref(new windwow)
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