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.
"The quadratic complete intersections associated with the action of the symmetric group." Illinois J. Math. 59 (1) 99 - 113, Spring 2015. https://doi.org/10.1215/ijm/1455203161