Zero dimensional Gorenstein algebras with the action of the symmetric group $S_k$
Preprint Series # 720 Morita, Hideaki and Watanabe, Junzo Zero dimensional Gorenstein algebras with the action of the symmetric group $S_k$. (2005); AbstractWe consider irreducible decompositions of certain Artinian algebras with
the action of the symmetric group.
The equidegree monomial complete intersection can be thought of as a kfold
tensor of an n dimensional vector space.
Otherwise put the tensor space can be given a commutative ring structure.
From this view point we show that, in the case n=2 or k=2,
the strong Lefschetz property can be
used efficiently to decompose the algebra into irreducible components.
We apply the result to determin a minimal generating set of certain
Gorenstein ideal.
Also we show that the Hilbert function of certain ring of invariants is a
qanolog of the binomial coefficent.
