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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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