Skip to main content

Invariants of Representations

  • Chapter

Part of the book series: NATO ASI Series ((ASIC,volume 279))

Abstract

Explicit Brauer Induction is a canonical form for Brauer’s induction theorem. It is designed for use in the construction of invariants of representations from invariants of one-dimensional characters. This paper gives a number of further applications including some new ‘change of field’ maps between representation rings, the behaviour of the canonical form wwith respect to Adams operations and a description of a refinement of Explicit Brauer Induction to produce canonical ‘monomial resolutions’ of representations of finite groups.

Research partially supported by NSERC grant #A4633.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   379.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arthur, J.G. and Clozel, L.: ‘Base change for GL(n)’, University of Toronto preprint, 1986.

    Google Scholar 

  2. Atiyah, M.F.: ‘Characters and cohomology of finite groups’, Pub. Math. I.H.E.S., Paris, 9, 23–64, 1961.

    MathSciNet  Google Scholar 

  3. Benson, D.: ‘Modular representation theory — new trends and methods’, Lecture Notes in Mathematics 1081, Springer-Verlag.

    Google Scholar 

  4. Bredon, G.E.: ‘Equivariant cohomology theories’, Lecture Notes in Mathematics 34, Springer-Verlag.

    Google Scholar 

  5. Cartier, P.: ‘Representations of p-adic groups — a survey’, Proc. Symp. Pure Math. A.M.Soc. 33, Part 1, 111–155.

    Google Scholar 

  6. Clozel, L: ‘Théorème d’Atiyah-Bott pour les variétés p-adiques et caractères des groupe réductifs’, preprint 1987.

    Google Scholar 

  7. Dwyer, W.G., Friedlander, E.M., Snaith, V.P., Thomason, R.W.: ‘Algebraic K-theory eventually surjects onto topological K-theory’, Inventiones Math. 66, 1982, 481–491.

    Article  MathSciNet  MATH  Google Scholar 

  8. Friedlander, E.M., ‘Étale K-theory II’, Ann. Sci. Ec. Norm. Sup., 4e serie, t. 15, 231–256, 1982.

    MathSciNet  MATH  Google Scholar 

  9. Fröhlich, A.: Tame representations of local Weil groups and of chain groups of local principal orders, Heidelberger Akad. der Wiss. Math. 3, 1986.

    MATH  Google Scholar 

  10. Fulton, W. and MacPherson, R.: ‘Characteristic classes of direct image bundles for covering maps’; Annals of Maths. 125, 1–92, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  11. Gelbart, S.: ‘An elementary introduction to the Langlands programme’, Bull. A.M.Soc., 10, 2, 177–219, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  12. Gérardin, P. and Labesse, J-P., ‘The solution of a base change problem for GL(2) (following Langlands, Saito, Shintani)’, Proc. Symp. Proc. Math. A.M.Soc. Part II, 115–133.

    Google Scholar 

  13. Green, J.A., ‘The characters of the finite general linear groups’; Trans. A.M.Soc. 80, 402–447, 1955.

    Article  MATH  Google Scholar 

  14. Green, J.A., Polynomial representations of GL n , Lecture Notes in Mathematics 830, Springer Verlag.

    Google Scholar 

  15. Hsiang, W.C. and Rees, H.D., ‘Miscenko’s work on Novikov’s conjecture’, A.M.Soc. Contemporary Math. 110, 77–98, 1981.

    Google Scholar 

  16. Iwasawa, K., Local class field theory. Oxford Math. Monographs, 1986.

    MATH  Google Scholar 

  17. Kahn, B., ‘Classes de Stiefel-Whitney de formes quadratiques et de représentations — Galoisiennes reélles’; Inventiones Math. 78, 223–256, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  18. Kato, K., ‘A generalisation of local class field theory using K-groups’, J. Fac. Sci. Univ. Tokyo. Sect. 1A 26, 303–376, 1979 and

    MATH  Google Scholar 

  19. Kato, K., ‘A generalisation of local class field theory using K-groups’, J. Fac. Sci. Univ. Tokyo. Sect. 1A 27, 603–683, 1980.

    MATH  Google Scholar 

  20. Kondo, T., ‘On Gaussian sums attached to the general linear groups over finite fields’, J. Math. Soc. Japan, 15, 3, 244–255, 1963.

    Article  MathSciNet  MATH  Google Scholar 

  21. Koslowski, A., “The Evens-Kahn formula for the total Stiefel-Whitney class”, Proc. A.M.Soc. 2, 91, 309–313, 1984.

    Article  Google Scholar 

  22. Langlands, R.P., Base change for GL(2), Annals of Math. Study 96, Princeton University Press.

    Google Scholar 

  23. Macdonald, I.G., ‘Zeta functions attached to finite general linear groups’, Math. Ann. 249, 1–15, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  24. Milnor, J.W., ‘Algebraic K-theory and quadratic forms’, Inventiones Math. 9, 318–344, 1970.

    Article  MathSciNet  MATH  Google Scholar 

  25. Serre, J-P., Local fields. Grad. Texts in Maths, 67, Spr inger-Verlag, 1979.

    Google Scholar 

  26. Serre, J-P., Linear representations of finite groups, Grad. Text in Maths. 42, Springer-Verlag, 1977.

    MATH  Google Scholar 

  27. Snaith, V.P., ‘Explicit Brauer Induction’, to appear in Inventiones Math.

    Google Scholar 

  28. Snaith, V.P., ‘Applications of Explicit Brauer Induction’, Proc. Symp. Pure Math. A.M.Soc. 47, Part 2, 495–531, 1987.

    MathSciNet  Google Scholar 

  29. Snaith, V.P., Topological methods in Galois representation theory. C.M.Soc. Monograph Series, Wiley, 1989.

    MATH  Google Scholar 

  30. Snaith, V.P., ‘A local construction of the local root numbers’, to appear Proc. Conf. Théorie des Nombres, Université Laval, 1987.

    Google Scholar 

  31. Snaith, V.P., ‘On the classifying spaces of Galois groups’, Proc. Can. Math. Soc. Conf. on algebraic topology, St. John’s, Newfoundland, 1983, A.M.Soc. Contemp. Math. Series 37, 145–148, 1985.

    MathSciNet  Google Scholar 

  32. Snaith, V.P., Algebraic K-theory and Localised stable homotopy theory. Mem. A.M.Soc. 280, 1983.

    Google Scholar 

  33. Snaith, V.P., ‘Unitary K-theory and the Lichtenbaum-Quillen Conjecture on the algebraic K-theory of schemes’, Prof. Conf. Alg. Top. Aarhus, Lecture Notes in Mathematics 1051, Springer-Verlag, 1982.

    Google Scholar 

  34. Snaith, V.P., ‘A construction of the Deligne-Langlands local root numbers of orthogonal representations’, to appear in Topology.

    Google Scholar 

  35. Springer, T.A., Invariant theory. Lecture Notes in Mathematics 585, Springer Verlag.

    Google Scholar 

  36. Thomason, R.W., ‘Algebraic K-theory and étale cohomology’, Ann. Sci. Ec. Norm. Sup. 18, 437–552, 1985.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Kluwer Academic Publishers

About this chapter

Cite this chapter

Snaith, V. (1989). Invariants of Representations. In: Jardine, J.F., Snaith, V.P. (eds) Algebraic K-Theory: Connections with Geometry and Topology. NATO ASI Series, vol 279. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2399-7_15

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-2399-7_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7580-0

  • Online ISBN: 978-94-009-2399-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics