Duke Mathematical Journal

Kazhdan-Lusztig conjecture for affine Lie algebras with negative level

Masaki Kashiwara and Toshiyuki Tanisaki

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Article information

Duke Math. J., Volume 77, Number 1 (1995), 21-62.

First available in Project Euclid: 20 February 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 17B67: Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
Secondary: 17B10: Representations, algebraic theory (weights)


Kashiwara, Masaki; Tanisaki, Toshiyuki. Kazhdan-Lusztig conjecture for affine Lie algebras with negative level. Duke Math. J. 77 (1995), no. 1, 21--62. doi:10.1215/S0012-7094-95-07702-3. https://projecteuclid.org/euclid.dmj/1077286145

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  • [BB] A. Beilinson and J. Bernstein, Localisation de $g$-modules, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981), no. 1, 15–18.
  • [BBD] A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and Topo logy on Singular Spaces I (Luminy, 1981), Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171.
  • [BK] J.-L. Brylinski and M. Kashiwara, Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math. 64 (1981), no. 3, 387–410.
  • [C1] L. Casian, Kazhdan-Lusztig multiplicity formulas for Kac-Moody algebras, C. R. Acad. Sci. Paris Sér. I Math. 310 (1990), no. 6, 333–337.
  • [C2] L. Casian, Kazhdan-Lusztig conjecture in the negative level case (Kac-Moody algebras of affine type), preprint.
  • [Kac] V. Kac, Infinite Dimensional Lie Algebras, 3rd ed., Cambridge Univ. Press, Cambridge, 1990.
  • [KK] V. Kac and D. Kazhdan, Structure of representations with highest weight of infinite-dimensional Lie algebras, Adv. in Math. 34 (1979), no. 1, 97–108.
  • [KP] V. Kac and D. Peterson, Infinite flag varieties and conjugacy theorems, Proc. Nat. Acad. Sci. U.S.A. 80 (1983), no. 6 i., 1778–1782.
  • [K1] M. Kashiwara, The flag manifold of Kac-Moody Lie algebra, Algebraic Analysis, Geometry and Number Theory (Baltimore, MD, 1988), Johns Hopkins Univ. Press, Baltimore, 1989, pp. 161–190.
  • [K2] M. Kashiwara, Kazhdan-Lusztig conjecture for a symmetrizable Kac-Moody Lie algebra, The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Birkhäuser Boston, Boston, MA, 1990, pp. 407–433.
  • [KT] M. Kashiwara and T. Tanisaki, Kazhdan-Lusztig conjecture for symmetrizable Kac-Moody Lie algebra II. Intersection cohomologies of Schubert varieties, Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory (Paris, 1989), Prog. Math., vol. 92, Birkhäuser, Boston, 1990, pp. 159–195.
  • [KL1] D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184.
  • [KL2] 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., vol. 36, Amer. Math. Soc., Providence, R.I., 1980, pp. 185–203.
  • [Ku] S. Kumar, Toward proof of Lusztig's conjecture concerning negative level representations of affine Lie algebras, J. Algebra 164 (1994), no. 2, 515–527.
  • [L] G. Lusztig, On quantum groups, J. Algebra 131 (1990), no. 2, 466–475.
  • [M1] O. Mathieu, Formules de caractères pour les algèbres de Kac-Moody générales, Astérisque (1988), no. 159-160, 267.
  • [M2] O. Mathieu, Construction d'un groupe de Kac-Moody et applications, Compositio Math. 69 (1989), no. 1, 37–60.
  • [S] M. Saito, Mixed Hodge modules, Publ. Res. Inst. Math. Sci. 26 (1990), no. 2, 221–333.
  • [T] J. Tits, Groups and group functors attached to Kac-Moody data, Workshop Bonn 1984 (Bonn, 1984), Lecture Notes in Math., vol. 1111, Springer-Verlag, Berlin, 1985, pp. 193–223.

See also

  • See also: Masaki Kashiwara, Toshiyuki Tanisaki. Kazhdan-Lusztig conjecture for affine Lie algebras with negative level II: Nonintegral case. Duke Math. J. Vol. 84, No. 3 (1996), pp. 771–813.