Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups

Abstract

For the coinvariant rings of finite Coxeter groups of types other than H${}_4$, we show that a homogeneous element of degree one is a strong Lefschetz element if and only if it is not fixed by any reflections. We also give the necessary and sufficient condition for strong Lefschetz elements in the invariant subrings of the coinvariant rings of Weyl groups.

18 pages

References in corpus (1)

• The strong Lefschetz property of the coinvariant ring of the Coxeter group of type H4

Cited by in corpus (7)

• The strong Lefschetz property of the coinvariant ring of the Coxeter group of type H4
• The Hilbert series of the superspace coinvariant ring
• Free extensions and Lefschetz properties, with an application to rings of relative coinvariants
• Lefschetz Properties and Hyperplane Arrangements
• Lefschetz theory for exterior algebras and fermionic diagonal coinvariants
• Power sum decompositions of defining equations of reflection arrangements
• The strong Lefschetz property for coinvariant rings of finite reflection groups