Inventiones mathematicae

, Volume 87, Issue 1, pp 153–215 | Cite as

Proof of the Deligne-Langlands conjecture for Hecke algebras

  • David Kazhdan
  • George Lusztig


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  1. [A] Atiyah, M.F.: Global theory of elliptic operators. Proc. Int. Conf. Funct. Anal. Rel. Topics, Tokyo 1969Google Scholar
  2. [AS] Atiyah, M.F., Segal, G.B.: EquivariantK-theory and completion. J. Differ. Geom.3, 1–18 (1969)Google Scholar
  3. [BV] Barbash, D., Vogan, D.: Unipotent representation of complex semisimple groups. Ann. Math.121, 41–110 (1985)Google Scholar
  4. [BFM] Baum, P., Fulton, W., MacPherson, R.: Riemann-Roch and topologicalK-theory for singular varieties. Acta Math.143, 155–192 (1979)Google Scholar
  5. [BZ] Bernstein, J., Zelevinskii, A.V.: Induced representations of reductivep-adic groups, I. Ann. Sci. E.N.S.10, 441–472 (1977)Google Scholar
  6. [BS] Beynon, W.M., Spaltenstein, N.: Green functions of finite Chevalley groups of typeE n (n=6, 7, 8). J. Algebra88, 584–614 (1984)Google Scholar
  7. [BB] Bialynicky-Birula, A.: Some theorems on actions of algebraic groups. Ann. Math.98, 480–497 (1973)Google Scholar
  8. [BW] Borel, A., Wallach, N.: Continuous cohomology, discrete subgroups and representations of reductive groups. Ann. Math. Stud.94 (1980), Princeton Univ. PressGoogle Scholar
  9. [G] Ginsburg, V.: Lagrangian construction for representations of Hecke algebras. (Preprint 1984)Google Scholar
  10. [H] Hironaka, H.: Bimeromorphic smoothing of a complex analytic space. Acta Math. Vietnam.2, (no2), Hanoi 1977Google Scholar
  11. [K] Kasparov, G.G.: Topological invariants of elliptic operators I.,K-homology. Izv. Akad. Nauk. SSSR39, 796–838 (1975)Google Scholar
  12. [KL1] Kazhdan, D., Lusztig, G.: A topological approach to Springer's representations. Adv. Math.38, 222–228 (1980)Google Scholar
  13. [KL2] Kazhdan, D., Lusztig, G.: EquivariantK-theory and representations of Hecke algebras II. Invent. Math.80, 209–231 (1985)Google Scholar
  14. [Ko] Kostant, B.: The principal 3-dimensional subgroup and the Betti numbers of a complex Lie group. Am. J. Math.81, 973–1032 (1959)Google Scholar
  15. [La] Langlands, R.P.: Problems in the theory of automorphic forms Lect. Modern Anal. Appl., Lect. Notes Math., vol. 170, pp. 18–86. Berlin-Heidelberg-New York: Springer 1970Google Scholar
  16. [L1] Lusztig, G.: Some examples of square integrable representations of semisimplep-adic groups. Trans. Am. Math. Soc.277, 623–653 (1983)Google Scholar
  17. [L2] Lusztig, G.: Cells in affine Weyl groups. In: Algebraic groups and related topics, Hotta, R. (ed.), Advanced Studies in Pure Mathematics, vol. 6. Kinokunia, Tokyo and North-Holland, Amsterdam, 1985Google Scholar
  18. [L3] Lusztig, G.: Character sheavesV. Adv. Math.61, 103–155 (1986)Google Scholar
  19. [L4] Lusztig, G.: EquivariantK-theory and representations of Hecke algebras. Proc. Am. Math. Soc.94, 337–342 (1985)Google Scholar
  20. [M] Mostow, G.D.: Fully reducible subgroups of algebraic groups. Am. J. Math.78, 200–221 (1956)Google Scholar
  21. [Se] Segal, G.B.: EquivariantK-theory. Publ. Math. IHES34, 129–151 (1968)Google Scholar
  22. [Sh] Shoji, T.: On the Green polynomials of classical groups. Invent. math.74, 239–264 (1983)Google Scholar
  23. [Sl] Slodowy, P.: Four lectures on simple groups and singularities. Commun. Math. Inst., Rijksuniv. Utr.11 (1980)Google Scholar
  24. [Sn] Snaith, V.: On the Künneth spectral sequence in equivariantK-theory. Proc. Camb. Philos. Soc.72, 167–177 (1972)Google Scholar
  25. [St] Steinberg, R.: On a theorem of Pittie. Topology14, 173–177 (1975)Google Scholar
  26. [T1] Thomason, R.: AlgebraicK-theory of group scheme actions. Proc. Topol. Conf. in honor J. Moore, Princeton 1983Google Scholar
  27. [T2] Thomason, R.: Comparison of equivariant algebraic and topologicalK-theory. PreprintGoogle Scholar
  28. [Z1] Zelevinskii, A.V.: Induced representations of reductivep-adic groups. II. On irreducible representations ofGL n. Ann. Sci. E.N.S.13, 165–210 (1980)Google Scholar
  29. [Z2] Zelevinskii, A.V.: Ap-adic analogue of the Kazhdan-Lusztig conjecture. Funkts. Anal. Prilozh.15, 9–21 (1981)Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • David Kazhdan
    • 1
  • George Lusztig
    • 2
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Department of MathematicsM.I.T.CambridgeUSA

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