Symmetric Spaces over a Finite Field

  • George Lusztig
Part of the Progress in Mathematics book series (MBC, volume 88)


Let G be a (connected) reductive group defined over a finite field F q (q odd) with a given involution θ:GG defined over F q . The pair (G, θ) will be called a symmetric space (over F q), we shall fix a closed subgroup K of the fixed point set G θ such that K is defined over F q and K contains the identity component (G θ )0 of .


Symmetric Space Finite Field Reductive Group Maximal Torus Closed Subgroup 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    E. Bannai, N. Kawanaka, S.Y. Song, The character table of the Hecke algebra H(GL 2n(Fq)iSp2n(F q)), preprint.Google Scholar
  2. [2]
    P. Deligne, G. Lusztig, Representations of reductive groups over finite fields, Ann. Math. 103 (1976), 103–161.CrossRefMATHMathSciNetGoogle Scholar
  3. [3]
    G. Lusztig, Representations of finite Chevalley groups, C.B.M.S. Regional Conf. Series in Math. 39, Amer. Math. Soc, 1978.MATHGoogle Scholar
  4. [4]
    T.A. Springer, Algebraic groups with involutions, in Algebraic Groups and Related Topics, Adv. Studies in Pure Math 6, Kinokuniya and North Holland, 1985.Google Scholar
  5. [5]
    R. Steinberg, Endomorphisms of linear algebraic groups, Mem. Amer Math. Soc. 80 (1968).Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • George Lusztig
    • 1
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations