We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring , thereby answering a classical question coming from works of F. Junker [J1, J2, J3] in the late nineteen century and then implicitly in H. Weyl book “The classical groups” [W].
Si est un anneau commutatif, on présente par générateurs et relations, l’algèbre des fonctions multisymétriques à coefficients dans , de façon à répondre à une question classique liée aux travaux de F. Junker [J1, J2, J3] et implicitement à ceux de H. Weyl [W].
Keywords: invariants theory, symmetric functions, representations of symmetric groups
Mot clés : théorie des invariants, polynômes symétriques, représentations du groupe symétrique
@article{AIF_2005__55_3_717_0, author = {Vaccarino, Francesco}, title = {The ring of multisymmetric functions}, journal = {Annales de l'Institut Fourier}, pages = {717--731}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {3}, year = {2005}, doi = {10.5802/aif.2111}, mrnumber = {2149400}, zbl = {1062.05143}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2111/} }
TY - JOUR AU - Vaccarino, Francesco TI - The ring of multisymmetric functions JO - Annales de l'Institut Fourier PY - 2005 SP - 717 EP - 731 VL - 55 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2111/ DO - 10.5802/aif.2111 LA - en ID - AIF_2005__55_3_717_0 ER -
%0 Journal Article %A Vaccarino, Francesco %T The ring of multisymmetric functions %J Annales de l'Institut Fourier %D 2005 %P 717-731 %V 55 %N 3 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2111/ %R 10.5802/aif.2111 %G en %F AIF_2005__55_3_717_0
Vaccarino, Francesco. The ring of multisymmetric functions. Annales de l'Institut Fourier, Volume 55 (2005) no. 3, pp. 717-731. doi : 10.5802/aif.2111. http://archive.numdam.org/articles/10.5802/aif.2111/
[A] The mod 2 cohomology rings of the symmetric groups and invariants, Topology (2002), pp. 57-84 | MR | Zbl
[B] Elements of mathematics - Algebra II Chapters 4-7, Springer-Verlag, Berlin, 1988 | MR
[D] Multisymmetric functions, Beiträge Algebra Geom., Volume 40 (1999) no. 1, pp. 27-51 | MR | Zbl
[F] A new degree bound for vector invariants of symmetric groups, Trans. Am. Math. Soc., Volume 350 (1998), pp. 1703-1712 | DOI | MR | Zbl
[G] Discriminants, resultants and multidimensional determinants, Birkahuser, Boston, 1994 | MR | Zbl
[J1] Die Relationen, welche zwischen den elementaren symmetrischen Functionen bestehen, Math. Ann., Volume 38 (1891), pp. 91-114 | DOI | JFM | MR
[J2] Über symmetrische Functionen von mehreren Reihen von Veränderlichen, Math. Ann., Volume 43 (1893), pp. 225-270 | DOI | JFM | MR
[J3] Die symmetrische Functionen und die Relationen zwischen den Elementarfunctionen derselben, Math. Ann., Volume 45 (1894), pp. 1-84 | DOI | JFM | MR
[M] Symmetric Functions and Hall Polynomials - second edition, Oxford mathematical monograph (1995) | MR | Zbl
[W] The classical groups, Princeton University Press, Princeton N.J., 1946 | MR | Zbl
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