Skip to main content

A survey on Hall-Littlewood functions and their applications to representation theory

Fonctions Symétriques

Part of the Lecture Notes in Mathematics book series (LNM,volume 579)

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight 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. I.J. DAVIES: "Enumeration of certain subgroups of Abelian p-groups", Proc. Edinburgh Math. Soc. (2), 13 (1962) 1–4.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. J.A. GREEN: "The characters of the finite general linear groups", Trans. American Math. Soc. 80 (1955) 402–447.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. _____ "Les polynomes de Hall et les caracteres des groupes GL (n,q)", Colloque d'algebre superieure (Brussels 1956) 207–215.

    Google Scholar 

  4. _____ "Symmetric functions and p-modules (lecture notes, Manchester 1962).

    Google Scholar 

  5. P. HALL: "The algebra of partitions", Proc. 4th Canadian Math. Congress, Banff (1957), (1959), 147–159.

    Google Scholar 

  6. G.D. JAMES: "A characteristic-free approach to the representation theory of Sn" (to appear).

    Google Scholar 

  7. T. KLEIN: "The multiplication of Schur functions and extensions of p-modules". J. London Math. Soc. 43 (1968) 280–284.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. _____ "The Hall Polynomial", J. of Algebra 12 (1969), 61–78.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. T. KONDO "On Gaussian sums attached to the general linear groups over finite fields", J. Math. Soc. Japan 15 (1963), 244–255.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. D.E. LITTLEWOOD: "The theory of group characters and matrix representations of groups", (Oxford, 1950).

    Google Scholar 

  11. _____ "On certain symmetric functions", Proc. London Math. Soc. (3) 11 (1961), 485–498.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. D.E. LITTLEWOOD and A.R. RICHARDSON: "Group characters and algebra", Phil. Trans. Roy. Soc. A. 233, (1934), 99–141.

    CrossRef  MATH  Google Scholar 

  13. I.G. MACDONALD: "Spherical functions in a group of p-adic type" Publications of the Ramanujan Institute No. 2.

    Google Scholar 

  14. _____ "Hall polynomials", Lecture notes (Warwick 1973).

    Google Scholar 

  15. A.O. MORRIS: "The spin representation of the symmetric group", Proc. London Math. Soc. (3) 12 (1962), 55–76.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. _____ "On Q-functions", J. London Math. Soc. 37 (1962), 445–455.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. _____ "The characters of the group GL (n, q)", Math. Zeits. 81 (1963), 112–123.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. _____ "The multiplication of Hall functions", Proc. London Math. Soc. (3) 13 (1963), 733–742.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. _____ "A note on the multiplication of Hall functions," J. London Math. Soc. 39 (1964), 481–488.

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. _____ "A note on symmetric functions", American Math. Monthly 71 (1964), 50–53.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. _____ "On an algebra of symmetric functions", Quart. J. Math. Oxford (2), 16 (1965), 53–64.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. _____ "A note on lemmas of Green and Kondo", Proc. Camb. Phil. Soc. 63 (1967), 83–85.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. F.D. MURNAGHAN: "The theory of group representations", (Baltimore, 1938).

    Google Scholar 

  24. J.B. OLSSON: "On the blocks of GL(n,q),I", Trans. Amer. Math. Soc. (to appear).

    Google Scholar 

  25. _____"On the blocks of GL(n,q),II" (Preprint).

    Google Scholar 

  26. O. PERRON: "Über Potenzsummen", Math. Zeits 64 (1956), 103–114.

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. G. de B. ROBINSON: "Representation theory of the symmetric group". (Edinburgh 1961).

    Google Scholar 

  28. I. SCHUR: "Über die Darstellung der symmetrischen und der alternierden Gruppe durch gebrochene lineare Substitutionen", J. Reine Angew Math. 139 (1911), 155–250.

    MathSciNet  MATH  Google Scholar 

  29. R.P. STANLEY: "Theory and Applications of Plane Partitions, Part I", Studies in Applied Mathematics 1 (1971), 167–188.

    CrossRef  MATH  Google Scholar 

  30. G.P. THOMAS: "Combinatorial proof of the Littlewood-Richardson rule", (to appear).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1977 Springer-Verlag

About this paper

Cite this paper

Morris, A.O. (1977). A survey on Hall-Littlewood functions and their applications to representation theory. In: Foata, D. (eds) Combinatoire et Représentation du Groupe Symétrique. Lecture Notes in Mathematics, vol 579. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090015

Download citation

  • DOI: https://doi.org/10.1007/BFb0090015

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08143-2

  • Online ISBN: 978-3-540-37385-8

  • eBook Packages: Springer Book Archive