## Crystal bases for the quantum superalgebra $U_q(\mathfrak {gl}(m,n))$

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- by Georgia Benkart, Seok-Jin Kang and Masaki Kashiwara
- J. Amer. Math. Soc.
**13**(2000), 295-331 - DOI: https://doi.org/10.1090/S0894-0347-00-00321-0
- Published electronically: January 31, 2000
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## 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.## References

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## Bibliographic 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
- 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. - © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1694051