A geometric setting for the quantum deformation of $GL_n$

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A geometric setting for the quantum deformation of $GL_n$

A. A. Beilinson, G. Lusztig, and R. MacPherson

Source: Duke Math. J. Volume 61, Number 2 (1990), 655-677.

First Page: Show

Primary Subjects: 17B37

Secondary Subjects: 16S30, 20G99

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077296831
Mathematical Reviews number (MathSciNet): MR1074310
Zentralblatt MATH identifier: 0713.17012
Digital Object Identifier: doi:10.1215/S0012-7094-90-06124-1

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References

[1] R. Dipper and S. Donkin, Quantum $GL_n$, preprint.

[2] V. G. Drinfeld, Quantum groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), Amer. Math. Soc., Providence, RI, 1987, pp. 798–820.

Mathematical Reviews (MathSciNet): MR89f:17017

Zentralblatt MATH: 0667.16003

[3] M. Jimbo, A $q$-analogue of $U(\germ g\germ l(N+1))$, Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), no. 3, 247–252.

Mathematical Reviews (MathSciNet): MR87k:17011

Zentralblatt MATH: 0602.17005

Digital Object Identifier: doi:10.1007/BF00400222

[4] D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184.

Mathematical Reviews (MathSciNet): MR81j:20066

Zentralblatt MATH: 0499.20035

Digital Object Identifier: doi:10.1007/BF01390031

[5] D. Kazhdan and G. Lusztig, Schubert varieties and Poincaré duality, Geometry of the Laplace operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979), Proc. Sympos. Pure Math., XXXVI, Amer. Math. Soc., Providence, R.I., 1980, pp. 185–203.

Mathematical Reviews (MathSciNet): MR84g:14054

Zentralblatt MATH: 0461.14015

[6] G. Lusztig, Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra, J. Amer. Math. Soc. 3 (1990), no. 1, 257–296.

Mathematical Reviews (MathSciNet): MR91e:17009

Zentralblatt MATH: 0695.16006

Digital Object Identifier: doi:10.2307/1990988

JSTOR: links.jstor.org

[7] G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), no. 2, 447–498.

Mathematical Reviews (MathSciNet): MR90m:17023

Zentralblatt MATH: 0703.17008

Digital Object Identifier: doi:10.2307/1990961

JSTOR: links.jstor.org