Crystal bases for the quantum superalgebra

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

Abstract | References | Similar Articles | Additional Information

A crystal base theory is introduced for the quantized enveloping algebra of the general linear Lie superalgebra , 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