和地　輝仁   ワチ　アキヒト   WACHI Akihito    所　　属   釧路校    職　　名   教授 言語種別 英語 発行・発表の年月 2009 形態種別 学術雑誌 査読 査読あり 標題 Zero-dimensional Gorenstein algebras with the action of the symmetric group. 執筆形態 共著 掲載誌名 Rend. Semin. Mat. Univ. Padova 出版社・発行元 Seminario Matematico of the University of Padua 巻・号・頁 121,pp.45-71 著者・共著者 Zero-dimensional Gorenstein algebras with the action of the symmetric group. 概要 $A(n,k)$ is defined over an algebraically closed field $K$ of characteristic zero, namely the quotient of $K[x_1,...,x_k]$ by the ideal $(x_1^n,...,x_k^n)$. This can be identified with tensor space as a $(GL(n) x S_k)$-module. The main result is the determination of the Hilbert series for each isotypic component of $A(n,k)$ corresponding to the Specht modules $V^{\lambda}$. This is given by the $q$-analogue of the corresponding Weyl dimension formula associated to the partition $\lambda$.