Hilbert Functions of ${\mathfrak{S}}_n$-Stable Artinian Gorenstein Algebras

Abstract

We describe the graded characters and Hilbert functions of certain graded artinian Gorenstein quotients of the polynomial ring which are also representations of the symmetric group. Specifically, we look at those algebras whose socles are trivial representations and whose principal apolar submodules are generated by the sum of the orbit of a power of a linear form.

Changed the final word in the title. Extended the statement and proof of Proposition 14. 20 pages long

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