Global crystal bases of quantum groups

Masaki Kashiwara

doi:10.1215/S0012-7094-93-06920-7

Duke Mathematical Journal

Duke Math. J.
Volume 69, Number 2 (1993), 455-485.

Global crystal bases of quantum groups

Masaki Kashiwara

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Article information

Source
Duke Math. J., Volume 69, Number 2 (1993), 455-485.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077293577

Digital Object Identifier
doi:10.1215/S0012-7094-93-06920-7

Mathematical Reviews number (MathSciNet)
MR1203234

Zentralblatt MATH identifier
0774.17018

Subjects
Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Secondary: 17B10: Representations, algebraic theory (weights) 81R50: Quantum groups and related algebraic methods [See also 16T20, 17B37]

Citation

Kashiwara, Masaki. Global crystal bases of quantum groups. Duke Math. J. 69 (1993), no. 2, 455--485. doi:10.1215/S0012-7094-93-06920-7. https://projecteuclid.org/euclid.dmj/1077293577

References

[BLM] A. A. Beilinson, G. Lusztig, and R. MacPherson, A geometric setting for the quantum deformation of $\rm GL\sb n$, Duke Math. J. 61 (1990), no. 2, 655–677.
Mathematical Reviews (MathSciNet): MR91m:17012
Zentralblatt MATH: 0713.17012
Digital Object Identifier: doi:10.1215/S0012-7094-90-06124-1
Project Euclid: euclid.dmj/1077296831
[K1] M. Kashiwara, Crystalizing the $q$-analogue of universal enveloping algebras, Comm. Math. Phys. 133 (1990), no. 2, 249–260.
Mathematical Reviews (MathSciNet): MR92b:17018
Zentralblatt MATH: 0724.17009
Digital Object Identifier: doi:10.1007/BF02097367
Project Euclid: euclid.cmp/1104201397
[K2] M. Kashiwara, On crystal bases of the $q$-analogue of universal enveloping algebras, Duke Math. J. 63 (1991), no. 2, 465–516.
Mathematical Reviews (MathSciNet): MR93b:17045
Zentralblatt MATH: 0739.17005
Digital Object Identifier: doi:10.1215/S0012-7094-91-06321-0
Project Euclid: euclid.dmj/1077295931
[K3] M. Kashiwara, Crystallizing the $q$-analogue of universal enveloping algebras, Proceedings of the International Congress of Mathematicians, Vol. I, II (Kyoto, 1990), Math. Soc. Japan, Tokyo, 1991, pp. 791–797.
Mathematical Reviews (MathSciNet): MR93b:17046
Zentralblatt MATH: 0749.17017
[L] G. Lusztig, Canonical bases in tensor products, Proc. Nat. Acad. Sci. U.S.A. 89 (1992), no. 17, 8177–8179.
Mathematical Reviews (MathSciNet): MR93j:17033
Zentralblatt MATH: 0760.17011
Digital Object Identifier: doi:10.1073/pnas.89.17.8177
JSTOR: links.jstor.org

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Global crystal bases of quantum groups

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