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Symmetric Spaces over a Finite Field

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

Abstract

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 .

Keywords

Symmetric Space Finite Field Reductive Group Maximal Torus Closed Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    E. Bannai, N. Kawanaka, S.Y. Song, The character table of the Hecke algebra H(GL 2n(Fq)iSp2n(F q)), preprint.Google Scholar
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    P. Deligne, G. Lusztig, Representations of reductive groups over finite fields, Ann. Math. 103 (1976), 103–161.CrossRefMATHMathSciNetGoogle Scholar
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    G. Lusztig, Representations of finite Chevalley groups, C.B.M.S. Regional Conf. Series in Math. 39, Amer. Math. Soc, 1978.MATHGoogle Scholar
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    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
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    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

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