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Invariants ofS 4 and the shape of sets of vectors

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Abstract

We study a representation ofS n that is related to the shape of sets of vectors in ℝn. We want to determine the invariants of this representation, and obtain a complete description for the case ofS 4.

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References

  1. Bayer, D., Stillman, M.: Macaulay: A system for computation in algebraic geometry and commutative algebra

  2. Bourbaki, N.: Groupes et algèbres de Lie, Chap. 4–6, Hermann, Paris, 1975

    Google Scholar 

  3. Chevalley, C.: Invariants of finite groups generated by reflections. Am. J. Math.77, 778–782 (1955)

    Google Scholar 

  4. Dixmier, J.: Sur les invariants du group symétrique dans certains représentations, II. In: Malliavin, M.-P. (ed.) Topics in Invariant Theory, Seminare P. Dubreil et M.-P. Malliavin 1989–1990, Lecture Notes in Math., vol. 1478, pp 1–34. Berlin, Heidelberg, New York: Springer 1991

    Google Scholar 

  5. Fulton, W., Harris, J.: Representation Theory, Graduate Text in Mathematics, vol. 129. Berlin, Heidelberg, New York: Springer 1991

    Google Scholar 

  6. Garsia, A.M., Procesi, C.: On certain gradedS n -modules and the q-Kostka polynomial. Adv. Math.94, 82–138 (1992)

    Google Scholar 

  7. Grove, L.C., McShane, J.M.: Polynomial invariants of finite groups Algebras Groups Geom.10, 1–12 (1993)

    Google Scholar 

  8. Jacobson, N.: Basic Algebra I. Oxford: W.H. Freeman 1985

    Google Scholar 

  9. Kemper, G.: The package for calculating rings of invariant, Maple share libary, Waterloo Maple Software, Maple V Release 3, Waterloo, Canada, 1994

    Google Scholar 

  10. Kraft, H.: Conjugacy classes and Weyl group representations. Tableauz de Young et foncteur de Schur en algèbre et géométrie (Torun, 1980), Asterisque 87–88, Société mathématique de France, 1981, pp. 191–205

  11. Stanley, R.P.: Invariants of finite groups and their applications to combinatorics. Bull. Am. Math. Soc. (N.S.)1, 475–511 (1979)

    Google Scholar 

  12. Stillman, M.: Methods for computing in algebraic geometry and commutative algebra. Acta Appl. Math.21, 77–103 (1990)

    Google Scholar 

  13. Sturmfels, B.: Algorithms in invariant theory. Wien, Springer 1993

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 0511, Singapore, Republic of Singapore

    Helmer Aslaksen & Shih-Ping Chan

  2. Department of Mathematics, University of Oslo, P.O. Box 1053, 0316, Blindern, Oslo, Norway

    Tor Gulliksen

Authors
  1. Helmer Aslaksen
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  2. Shih-Ping Chan
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  3. Tor Gulliksen
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Aslaksen, H., Chan, SP. & Gulliksen, T. Invariants ofS 4 and the shape of sets of vectors. AAECC 7, 53–57 (1996). https://doi.org/10.1007/BF01613616

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  • DOI: https://doi.org/10.1007/BF01613616

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