|
Young wall realization of crystal bases for classical Lie algebras
Author(s):
Seok-Jin
Kang;
Jeong-Ah
Kim;
Hyeonmi
Lee;
Dong-Uy
Shin
Journal:
Trans. Amer. Math. Soc.
356
(2004),
2349-2378.
MSC (2000):
Primary 81R50
Posted:
December 12, 2003
MathSciNet review:
2048521
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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.
References:
-
- 1.
- W. Fulton, Young Tableau: with applications to representation theory and geometry, Cambridge University Press, 1997. MR 99f:05119
- 2.
- J. Hong, S.-J. Kang, Introduction to Quantum Groups and Crystal Bases, Graduate Studies in Mathematics 42, Amer. Math. Soc., 2002. MR 2002m:17012
- 3.
- S.-J. Kang, Crystal bases for quantum affine algebras and combinatorics of Young walls, Proc. London Math. Soc. 86 (2003), 29-69.
- 4.
- S.-J. Kang, J.-H. Kwon, Fock space representations of quantum affine algebras and generalized Lascoux-Leclerc-Thibon algorithm, KIAS preprint M02011.
- 5.
- S.-J. Kang, K. C. Misra, Crystal bases and tensor product decompositions of
 -modules, J. Algebra 163 (1994), 675-691. MR 95f:17013 - 6.
- M. Kashiwara, Crystalizing the
 -analogue of universal enveloping algebras, Comm. Math. Phys. 133 (1990), 249-260. MR 92b:17018 - 7.
- -, On crystal bases of the
 -analogue of universal enveloping algebras, Duke Math. J. 63 (1991), 465-516. MR 93b:17045 - 8.
- -, Similarity of crystal bases, in Lie Algebras and Their Representations, Seoul (1995), S.-J. Kang, M.-H. Kim, I. Lee (eds.), Contemp. Math. 194 (1996), Amer. Math. Soc., 177-186. MR 97g:17013
- 9.
- M. Kashiwara, T. Nakashima, Crystal graphs for representations of the
 -analogue of classical Lie algebras, J. Algebra 165 (1994), 295-345. MR 95c:17025 - 10.
- J.-A. Kim, D.-U. Shin, Correspondence between Young walls and Young tableaux realizations of crystal bases for the classical Lie algebras, preprint math.QA/0303287.
- 11.
- H. Lee, Demazure crystals of type
 and Young walls, KIAS preprint M02007. - 12.
- P. Littelmann, Crystal graphs and Young tableaux, J. Algebra 175 (1995), 65-87. MR 96h:17022
- 13.
- -, Paths and root operators in representation theory, Ann. of Math. 142 (1995), 499-525. MR 96m:17011
- 14.
- -, A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras, Invent. Math. 116 (1994), 329-346. MR 95f:17023
- 15.
- I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford University Press, Oxford, 2nd ed., 1995. MR 96h:05207
- 16.
- T. Nakashima, Crystal base and a generalization of the Littlewood-Richardson rule for classical Lie algebras, Comm. Math. Phys. 154 (1993), 215-243. MR 94f:17015
Similar Articles:
Retrieve articles in Transactions of the American Mathematical
Society
with
MSC (2000):
81R50
Retrieve articles in all Journals with
MSC (2000):
81R50
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:
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
Posted:
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
Copyright of article:
Copyright
2003,
American Mathematical Society
|
