Hilbert Functions of \mathfrak S_n-Stable Artinian Gorenstein Algebras

2014/07/27 by Geramita, Anthony V., Hoefel, Andrew H., Wehlau, David L.
#05E10 #13D40 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.7228

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.

Related

• Hilbert functions of Gorenstein algebras associated to a pencil of forms
• Hilbert functions of graded algebras over Artinian rings
• Gorenstein algebras presented by quadrics
• Limits of graded Gorenstein algebras of Hilbert function (1,3^k,1)
• Artinian Gorenstein algebras of embedding dimension four: Components of PGor(H) for H=(1,4,7,..., 1)