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

DOI:
https://doi.org/10.1090/S0002-9947-03-03400-7

Published electronically:
December 12, 2003

MathSciNet review:
2048521

Full-text PDF

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.

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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:
https://doi.org/10.1090/S0002-9947-03-03400-7

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