Duke Mathematical Journal

An algebraic characterization of the affine canonical basis

Jonathan Beck, Vyjayanthi Chari, and Andrew Pressley

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Article information

Source
Duke Math. J. Volume 99, Number 3 (1999), 455-487.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077227911

Digital Object Identifier
doi:10.1215/S0012-7094-99-09915-5

Mathematical Reviews number (MathSciNet)
MR1712630

Zentralblatt MATH identifier
0964.17013

Subjects
Primary: 17B37: Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23]
Secondary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras

Citation

Beck, Jonathan; Chari, Vyjayanthi; Pressley, Andrew. An algebraic characterization of the affine canonical basis. Duke Math. J. 99 (1999), no. 3, 455--487. doi:10.1215/S0012-7094-99-09915-5. http://projecteuclid.org/euclid.dmj/1077227911.


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References

  • [B1] Jonathan Beck, Braid group action and quantum affine algebras, Comm. Math. Phys. 165 (1994), no. 3, 555–568.
  • [B2] Jonathan Beck, Convex bases of PBW type for quantum affine algebras, Comm. Math. Phys. 165 (1994), no. 1, 193–199.
  • [BFJ] Jonathan Beck, Igor B. Frenkel, and Naihuan Jing, Canonical basis and Macdonald polynomials, Adv. Math. 140 (1998), no. 1, 95–127.
  • [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.
  • [CP] Vyjayanthi Chari and Andrew Pressley, Quantum affine algebras at roots of unity, Represent. Theory 1 (1997), 280–328 (electronic).
  • [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.
  • [Dr] V. Drinfeld, A new realization of Yangians and quantum affine algebras, Soviet Math. Dokl. 36 (1988), 212–216.
  • [G] Howard Garland, Erratum: “The arithmetic theory of loop algebras”, J. Algebra 63 (1980), no. 1, 285.
  • [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.
  • [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.
  • [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.
  • [K] M. Kashiwara, On crystal bases of the $Q$-analogue of universal enveloping algebras, Duke Math. J. 63 (1991), no. 2, 465–516.
  • [L1] George Lusztig, Affine Hecke algebras and their graded version, J. Amer. Math. Soc. 2 (1989), no. 3, 599–635.
  • [L2] G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), no. 2, 447–498.
  • [L3] George Lusztig, Finite-dimensional Hopf algebras arising from quantized universal enveloping algebra, J. Amer. Math. Soc. 3 (1990), no. 1, 257–296.
  • [L4] G. Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras, J. Amer. Math. Soc. 4 (1991), no. 2, 365–421.
  • [L5] George Lusztig, Introduction to quantum groups, Progress in Mathematics, vol. 110, Birkhäuser Boston Inc., Boston, MA, 1993.
  • [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.
  • [L7] George Lusztig, Braid group action and canonical bases, Adv. Math. 122 (1996), no. 2, 237–261.
  • [M] I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1995, 2d ed.