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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Young wall realization of crystal bases for classical Lie algebras


Authors: Seok-Jin Kang, Jeong-Ah Kim, Hyeonmi Lee and Dong-Uy Shin
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 2349-2378
MSC (2000): Primary 81R50
Published electronically: December 12, 2003
MathSciNet review: 2048521
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Abstract: In this paper, we give a new realization of crystal bases for finite-dimensional irreducible modules over classical Lie algebras. The basis vectors are parameterized by certain Young walls lying between highest weight and lowest weight vectors.


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Additional Information

Seok-Jin Kang
Affiliation: School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongryangri 2 Dong, Dongdaemun-gu, Seoul 130-722, Korea
Email: sjkang@kias.re.kr

Jeong-Ah Kim
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-747, Korea
Email: jakim@math.snu.ac.kr

Hyeonmi Lee
Affiliation: School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongryangri 2 Dong, Dongdaemun-gu, Seoul 130-722, Korea
Email: hmlee@kias.re.kr

Dong-Uy Shin
Affiliation: School of Mathematics, Korea Institute for Advanced Study, 207-43 Cheongryangri 2 Dong, Dongdaemun-gu, Seoul 130-722, Korea
Email: shindong@kias.re.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03400-7
PII: S 0002-9947(03)03400-7
Received by editor(s): June 5, 2002
Received by editor(s) in revised form: April 2, 2003
Published electronically: December 12, 2003
Additional Notes: The first author’s research was supported by KOSEF Grant # 98-0701-01-5-L and the Young Scientist Award, Korean Academy of Science and Technology
The second, third, and fourth authors’ research was supported by KOSEF Grant # 98-0701-01-5-L and BK21 Mathematical Sciences Division, Seoul National University
Article copyright: © Copyright 2003 American Mathematical Society