Crystal bases for the quantum superalgebra 𝑈_{𝑞}(𝔤𝔩(𝔪,𝔫))

Benkart, Georgia; Kang, Seok-Jin; Kashiwara, Masaki

doi:10.1090/S0894-0347-00-00321-0

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
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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
Email: benkart@math.wisc.edu

Seok-Jin Kang
Affiliation: Department of Mathematics, Seoul National University, Seoul 151-742, Korea
Email: sjkang@math.snu.ac.kr

Masaki Kashiwara
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606–8502, Japan
Email: masaki@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S0894-0347-00-00321-0
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