Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups

Details Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups Strong Lefschetz elements of the coinvariant rings of finite Coxeter groups

2008-09-21

arxiv.org/abs/0809.3558v1

Mathematics

Representation Theory

18 pages

Scientific paper

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.

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