Dept. Math, Hokkaido Univ. EPrints Server

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);

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Abstract

We consider irreducible decompositions of certain Artinian algebras with the action of the symmetric group. The equi-degree monomial complete intersection can be thought of as a k-fold 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 q-anolog of the binomial coefficent.

Item Type:Preprint
Additional Information:60
Uncontrolled Keywords:Gorenstein algebra, symmetric group, Schur-Weyl duality, strong Lefschetz property, Specht polynomial, q-analogue, Hilbert function.
Subjects:20-xx GROUP THEORY AND GENERALIZATIONS
13-xx COMMUTATIVE RINGS AND ALGEBRAS
05-xx COMBINATORICS
ID Code:953