Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$
Authors:
Georgia Benkart, Seok-Jin Kang and Masaki Kashiwara
Journal:
J. Amer. Math. Soc. 13 (2000), 295-331
MSC (1991):
Primary 17B65, 17B37, 81R50, 05E10
DOI:
https://doi.org/10.1090/S0894-0347-00-00321-0
Published electronically:
January 31, 2000
MathSciNet review:
1694051
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: A crystal base theory is introduced for the quantized enveloping algebra of the general linear Lie superalgebra $\mathfrak {gl}(m,n)$, and an explicit realization of the crystal base is given in terms of semistandard tableaux.
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Additional Information
Georgia Benkart
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706–1388
MR Author ID:
34650
Email:
benkart@math.wisc.edu
Seok-Jin Kang
Affiliation:
Department of Mathematics, Seoul National University, Seoul 151-742, Korea
MR Author ID:
307910
Email:
sjkang@math.snu.ac.kr
Masaki Kashiwara
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606–8502, Japan
MR Author ID:
98845
Email:
masaki@kurims.kyoto-u.ac.jp
Keywords:
General linear Lie superalgebra,
quantized enveloping algebra,
crystal base,
semistandard tableau
Received by editor(s):
November 2, 1998
Received by editor(s) in revised form:
June 21, 1999
Published electronically:
January 31, 2000
Additional Notes:
The first author was supported in part by National Science Foundation Grant #DMS-9622447.
The second author was supported in part by the Basic Science Research Institute Program, Ministry of Education of Korea, BSRI-98-1414, and GARC-KOSEF at Seoul National University.
Article copyright:
© Copyright 2000
American Mathematical Society
