Hilbert Functions of $\mathfrak S_n$-Stable Artinian Gorenstein Algebras
Commutative Algebra
2016-03-22 v3
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.
Keywords
Cite
@article{arxiv.1407.7228,
title = {Hilbert Functions of $\mathfrak S_n$-Stable Artinian Gorenstein Algebras},
author = {Anthony V. Geramita and Andrew H. Hoefel and David L. Wehlau},
journal= {arXiv preprint arXiv:1407.7228},
year = {2016}
}
Comments
Changed the final word in the title. Extended the statement and proof of Proposition 14. 20 pages long