Advertisement

Morita Equivalence, GLn(Fq)-Modules, and the Steenrod Algebra

  • Nicholas J. Kuhn
Part of the Mathematical Sciences Research Institute Publications book series (MSRI, volume 27)

Abstract

The purpose of this announcement is to describe, on one hand, a new approach to the modular representation theory of the semigroup of n × n matrices M n (F q ) and its group of units GL n (F q ), and, on the other, a new approach to studying the category of unstable modules over the Steenrod “q th-power” operations. Perhaps most remarkable is that these two approaches are the same via a generalization of classical Morita equivalence.

Keywords

Unstable Module Full Subcategory Algebraic Topology Privileged Role Mathematical Science Research Institute 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AF]
    F.W. Anderson and K.R. Fuller, Rings and categories of modules, Springer Graduate Texts in Math. 13, 1974.Google Scholar
  2. [AGM]
    J.F. Adams, J.H. Gunawardena and H.R. Miller, The Segal conjecture for elementary abelian p-groups, Topology 24(1985), 435–460.CrossRefMATHMathSciNetGoogle Scholar
  3. [C]
    C. Carlsson, G.B. Segal’s Burnside ring conjecture for(ℤ2)k, Topology 22(1983), 83–103.CrossRefMATHMathSciNetGoogle Scholar
  4. [FS]
    V. Franjou and L. Schwartz, Reduced unstable A-modules and the modular representation theory of the symmetric groups, Preprint (1989).Google Scholar
  5. [HLS]
    H.W. Henn, J. Lannes and L. Schwartz, The categories of unstable modules and unstable algebras over the Steenrod algebra modulo nilpotent objects, Ann Scient. Ecole Norm. Sup. 23(1990), 593–624.Google Scholar
  6. [K]
    N.J. Kuhn, Generic representations of the finite general linear groups and the Steenrod algebra: I, II, III., Part I is a preprint. Parts II and III are in preparation.Google Scholar
  7. [LS]
    J. Lannes and L. Schwartz, Sur la structure des A-modules instables injectifs, Topology 28(1989), 153–169.CrossRefMATHMathSciNetGoogle Scholar
  8. [LS2]
    J. Lannes and L. Schwartz, Polynomial Functors and unstable A-modules, in preparation.Google Scholar
  9. [LZ]
    J. Lannes and S. Zarati, Foncteurs dérivés de la déstabilisation, Math. Zeit. 194(1987), 25–59.CrossRefMATHMathSciNetGoogle Scholar
  10. [Mac]
    I.G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford Math. Monographs, Oxford University Press, New York, 1979.Google Scholar
  11. [Ml]
    H.R. Miller, The Sullivan conjecture on maps from classifying spaces, Ann. Math. 120(1984), 39–87.CrossRefMATHGoogle Scholar
  12. [Mn]
    J. Milnor, The Steenrod algebra and its dual, Ann. Math. 67(1958), 150–171.CrossRefMATHMathSciNetGoogle Scholar
  13. [W]
    R.M. Wood, SplittingΣ(CP∞ ×…× CP∞) and the action of Steenrod squares S q i on the polynomial ringF2[x1,..., xn],, in “Algebraic Topology”—Barcelona 1986, Springer L. N. Math. 1298(1987), 237–255.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Nicholas J. Kuhn
    • 1
  1. 1.Department Of MathematicsUniversity of VirginiaCharlottesvilleUSA

Personalised recommendations