和地 輝仁
ワチ アキヒト WACHI Akihito 所 属 釧路校 職 名 教授 |
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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 $\lambda$. |