Illinois Journal of Mathematics

The quadratic complete intersections associated with the action of the symmetric group

Tadahito Harima, Akihito Wachi, and Junzo Watanabe

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Abstract

We prove that any quadratic complete intersection with a certain action of the symmetric group has the strong Lefschetz property over a field of characteristic zero. Furthermore, we discuss under what conditions its ring of invariants by a Young subgroup is a homogeneous complete intersection with a standard grading.

Article information

Source
Illinois J. Math., Volume 59, Number 1 (2015), 99-113.

Dates
Received: 23 February 2015
Revised: 2 November 2015
First available in Project Euclid: 11 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1455203161

Digital Object Identifier
doi:10.1215/ijm/1455203161

Mathematical Reviews number (MathSciNet)
MR3459630

Zentralblatt MATH identifier
1336.13009

Subjects
Primary: 13E10: Artinian rings and modules, finite-dimensional algebras
Secondary: 13F20: Polynomial rings and ideals; rings of integer-valued polynomials [See also 11C08, 13B25] 20B35: Subgroups of symmetric groups

Citation

Harima, Tadahito; Wachi, Akihito; Watanabe, Junzo. The quadratic complete intersections associated with the action of the symmetric group. Illinois J. Math. 59 (2015), no. 1, 99--113. doi:10.1215/ijm/1455203161. https://projecteuclid.org/euclid.ijm/1455203161


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References

  • I. M. Gelfand, M. M. Kapranov and A. V. Zelevinsky, Discriminants, resultants and multidimensional determinants, Birkhäuser, Boston, MA, 1994.
  • S. Goto, Invariant subrings under the action by a finite group generated by pseudo-reflections, Osaka J. Math. 15 (1978), no. 1, 47–50.
  • D. Grayson and M. Stillman, Macaulay2, available at http://www.math.uiuc.edu/Macaulay2/.
  • T. Harima and J. Watanabe, The strong Lefschetz property for Artinian algebras with non-standard grading, J. Algebra 311 (2007), no. 2, 511–537.
  • T. Harima, T. Maeno, H. Morita, Y. Numata, A. Wachi and J. Watanabe, The Lefschetz properties, Lecture Notes in Mathematics, vol. 2080, Springer-Verlag, Heidelberg, 2013.
  • H. Ikeda, Results on Dilworth and Ress numbers of Artinian local rings, Japan. J. Math. (N.S.) 22 (1996), no. 1, 147–158.
  • G. James and A. Kerber, The representation theory of the symmetric group, Encyclopedia of Mathematics and Its Applications, vol. 16, Addison-Weslay, Reading, MA, 1981.
  • H. Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1989.
  • B. Sagan, The symmetric group, 2nd ed., Graduate Texts in Mathematics, vol. 203, Springer-Verlag, New York, 2001.
  • L. Smith, The polynomial invariants of finite groups, Research Notes in Mathematics, vol. 6, A K Peters, Wellesley, MA, 1995.