An algebraic characterization of the affine canonical basis
Jonathan Beck, Vyjayanthi Chari, and Andrew Pressley
Source: Duke Math. J. Volume 99, Number 3
(1999), 455-487.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077227911
Mathematical Reviews number (MathSciNet): MR1712630
Zentralblatt MATH identifier: 0964.17013
Digital Object Identifier: doi:10.1215/S0012-7094-99-09915-5
References
[B1] Jonathan Beck, Braid group action and quantum affine algebras, Comm. Math. Phys. 165 (1994), no. 3, 555–568.
Mathematical Reviews (MathSciNet): MR95i:17011
Zentralblatt MATH: 0807.17013
Digital Object Identifier: doi:10.1007/BF02099423
Project Euclid: euclid.cmp/1104271413
[B2] Jonathan Beck, Convex bases of PBW type for quantum affine algebras, Comm. Math. Phys. 165 (1994), no. 1, 193–199.
Mathematical Reviews (MathSciNet): MR96b:17008
Zentralblatt MATH: 0828.17016
Digital Object Identifier: doi:10.1007/BF02099742
Project Euclid: euclid.cmp/1104271039
[BFJ] Jonathan Beck, Igor B. Frenkel, and Naihuan Jing, Canonical basis and Macdonald polynomials, Adv. Math. 140 (1998), no. 1, 95–127.
Mathematical Reviews (MathSciNet): MR2000k:33041
Zentralblatt MATH: 0924.17006
Digital Object Identifier: doi:10.1006/aima.1998.1763
[Bo] N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles, No. 1337, Hermann, Paris, 1968.
Mathematical Reviews (MathSciNet): MR39:1590
Zentralblatt MATH: 0186.33001
[CP] Vyjayanthi Chari and Andrew Pressley, Quantum affine algebras at roots of unity, Represent. Theory 1 (1997), 280–328 (electronic).
Mathematical Reviews (MathSciNet): MR98e:17018
Zentralblatt MATH: 0891.17013
Digital Object Identifier: doi:10.1090/S1088-4165-97-00030-7
[Da] Ilaria Damiani, La $R$-matrice pour les algèbres quantiques de type affine non tordu, Ann. Sci. École Norm. Sup. (4) 31 (1998), no. 4, 493–523.
Mathematical Reviews (MathSciNet): MR99g:17027
Zentralblatt MATH: 0911.17005
Digital Object Identifier: doi:10.1016/S0012-9593(98)80104-3
[Dr] V. Drinfeld, A new realization of Yangians and quantum affine algebras, Soviet Math. Dokl. 36 (1988), 212–216.
Zentralblatt MATH: 0667.16004
Mathematical Reviews (MathSciNet): MR914215
[G] Howard Garland, Erratum: “The arithmetic theory of loop algebras”, J. Algebra 63 (1980), no. 1, 285.
Mathematical Reviews (MathSciNet): MR81d:17008
Zentralblatt MATH: 0424.17009
[GL] I. Grojnowski and G. Lusztig, A comparison of bases of quantized enveloping algebras, Linear algebraic groups and their representations (Los Angeles, CA, 1992), Contemp. Math., vol. 153, Amer. Math. Soc., Providence, RI, 1993, pp. 11–19.
Mathematical Reviews (MathSciNet): MR94m:17012
Zentralblatt MATH: 1009.17502
[J] Naihuan Jing, On Drinfeld realization of quantum affine algebras, The Monster and Lie algebras (Columbus, OH, 1996), Ohio State Univ. Math. Res. Inst. Publ., vol. 7, de Gruyter, Berlin, 1998, pp. 195–206.
Mathematical Reviews (MathSciNet): MR99j:17021
Zentralblatt MATH: 0983.17013
[JKK] Nai Huan Jing, Seok-Jin Kang, and Yoshitaka Koyama, Vertex operators of quantum affine Lie algebras $U\sb q(D\sp (1)\sb n)$, Comm. Math. Phys. 174 (1995), no. 2, 367–392.
Mathematical Reviews (MathSciNet): MR96j:17022
Zentralblatt MATH: 0873.17026
Digital Object Identifier: doi:10.1007/BF02099607
Project Euclid: euclid.cmp/1104275298
[K] 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
[L1] George Lusztig, Affine Hecke algebras and their graded version, J. Amer. Math. Soc. 2 (1989), no. 3, 599–635.
Mathematical Reviews (MathSciNet): MR90e:16049
Zentralblatt MATH: 0715.22020
Digital Object Identifier: doi:10.2307/1990945
JSTOR: links.jstor.org
[L2] 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
[L3] George 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
[L4] G. Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras, J. Amer. Math. Soc. 4 (1991), no. 2, 365–421.
Mathematical Reviews (MathSciNet): MR91m:17018
Zentralblatt MATH: 0738.17011
Digital Object Identifier: doi:10.2307/2939279
JSTOR: links.jstor.org
[L5] George Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston Inc., Boston, MA, 1993.
Mathematical Reviews (MathSciNet): MR94m:17016
Zentralblatt MATH: 0788.17010
[L6] George Lusztig, Quantum groups at $v=\infty$, Functional analysis on the eve of the 21st century, Vol. 1 (New Brunswick, NJ, 1993), Progr. Math., vol. 131, Birkhäuser Boston, Boston, MA, 1995, pp. 199–221.
Mathematical Reviews (MathSciNet): MR97g:17014
Zentralblatt MATH: 0856.17013
[L7] George Lusztig, Braid group action and canonical bases, Adv. Math. 122 (1996), no. 2, 237–261.
Mathematical Reviews (MathSciNet): MR98g:17019
Zentralblatt MATH: 0861.17008
Digital Object Identifier: doi:10.1006/aima.1996.0061
[M] I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1995, 2d ed.
Mathematical Reviews (MathSciNet): MR96h:05207
Zentralblatt MATH: 0824.05059
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