The ring of multisymmetric functions

Francesco Vaccarino[1]

  • [1] Politecnico di Torino, dipartimento di Matematica, Corso Duca degli Abruzzi 24, 10129 Torino (Italy)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 3, page 717-731
  • ISSN: 0373-0956

Abstract

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We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring R , 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].

How to cite

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Vaccarino, Francesco. "The ring of multisymmetric functions." Annales de l’institut Fourier 55.3 (2005): 717-731. <http://eudml.org/doc/116205>.

@article{Vaccarino2005,
abstract = {We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring $R$, 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].},
affiliation = {Politecnico di Torino, dipartimento di Matematica, Corso Duca degli Abruzzi 24, 10129 Torino (Italy)},
author = {Vaccarino, Francesco},
journal = {Annales de l’institut Fourier},
keywords = {invariants theory; symmetric functions; representations of symmetric groups; invariant theory},
language = {eng},
number = {3},
pages = {717-731},
publisher = {Association des Annales de l'Institut Fourier},
title = {The ring of multisymmetric functions},
url = {http://eudml.org/doc/116205},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Vaccarino, Francesco
TI - The ring of multisymmetric functions
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 3
SP - 717
EP - 731
AB - We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring $R$, 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].
LA - eng
KW - invariants theory; symmetric functions; representations of symmetric groups; invariant theory
UR - http://eudml.org/doc/116205
ER -

References

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  1. M. Feschbach, The mod 2 cohomology rings of the symmetric groups and invariants, Topology (2002), 57-84 Zbl1039.20029MR1871241
  2. N. Bourbaki, Elements of mathematics - Algebra II Chapters 4-7, (1988), Springer-Verlag, Berlin Zbl1139.12001MR1080964
  3. J. Dalbec, Multisymmetric functions, Beiträge Algebra Geom. 40 (1999), 27-51 Zbl0953.05077MR1678567
  4. P. Fleischmann, A new degree bound for vector invariants of symmetric groups, Trans. Am. Math. Soc. 350 (1998), 1703-1712 Zbl0891.13002MR1451600
  5. I. Gelfand, M. Kapranov, A. Zelevinsky, Discriminants, resultants and multidimensional determinants, (1994), Birkahuser, Boston Zbl0827.14036MR1264417
  6. F. Junker, Die Relationen, welche zwischen den elementaren symmetrischen Functionen bestehen, Math. Ann. 38 (1891), 91-114 Zbl23.0156.02MR1510665
  7. F. Junker, Über symmetrische Functionen von mehreren Reihen von Veränderlichen, Math. Ann. 43 (1893), 225-270 Zbl25.0230.01MR1510811
  8. F. Junker, Die symmetrische Functionen und die Relationen zwischen den Elementarfunctionen derselben, Math. Ann. 45 (1894), 1-84 Zbl25.0230.02MR1510854
  9. I.G. Macdonald, Symmetric Functions and Hall Polynomials - second edition, Oxford mathematical monograph (1995) Zbl0487.20007MR1354144
  10. H. Weyl, The classical groups, (1946), Princeton University Press, Princeton N.J. Zbl0020.20601MR1488158

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