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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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참고문헌 (19)
참고문헌 신청
A. Lascoux / 1996 / Hecke algebras at roots of unity and crystal bases of quantum affine algebras / Communications in Mathematical Physics 181 (1) : 205 ~ 263
A. Mathas / 1999 / Iwahori-Hecke Algebras and Schur Algebras of the Symetric Group, Unibersity Lecture Series / American Mathematical Society : 15 ~
B. Leclerc / 1997 / q-deformed Fock spaces and modular representations of spin symmetric groups / Journal of Physics A 30 (17) : 6163 ~ 6176
G. James / 1990 / The Representation Theory of the Symmetric Group, With a foreword by P. M. Cohn. With an introduction by Gilbert de B. Robison. Encyclopedia of Mathematics and its Appl
G. Lusztig / 1990 / Canonical bases arising from quantized enveloping algebras / Journal of the American Mathematical Society 3 (2) : 447 ~ 498
A. Mathas / 1999 / Iwahori-Hecke Algebras and Schur Algebras of the Symetric Group, Unibersity Lecture Series / American Mathematical Society : 15 ~
B. Leclerc / 1997 / q-deformed Fock spaces and modular representations of spin symmetric groups / Journal of Physics A 30 (17) : 6163 ~ 6176
G. James / 1990 / The Representation Theory of the Symmetric Group, With a foreword by P. M. Cohn. With an introduction by Gilbert de B. Robison. Encyclopedia of Mathematics and its Appl
G. Lusztig / 1990 / Canonical bases arising from quantized enveloping algebras / Journal of the American Mathematical Society 3 (2) : 447 ~ 498
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