The strong Lefschetz property for coinvariant rings of finite reflection groups

TL;DR

This paper proves that the coinvariant ring of any finite reflection group possesses the strong Lefschetz property by establishing a key algebraic result and applying Schubert calculus techniques.

Contribution

It introduces a new algebraic result on deformed tensor products of Lefschetz algebras and applies it to prove the strong Lefschetz property for coinvariant rings.

Findings

Coinvariant rings of finite reflection groups have the strong Lefschetz property.

A deformed tensor product of Lefschetz algebras is itself Lefschetz.

Application of Schubert calculus is used to establish the main result.

Abstract

In this paper we prove that a deformed tensor product of two Lefschetz algebras is a Lefschetz algebra. We then use this result in conjunction with some basic Schubert calculus to prove that the coinvariant ring of a finite reflection has the strong Lefschetz property.