一类伪反射群的向量不变量与多重对称合偶
Vector invariants of a class of pseudo-reflection groups and multisymmetric syzygies
摘要：
在群的阶在基域上可逆的假设下，给出了一类伪反射群（包括$B_n$型外尔群）的多项式不变量的第一和第二基本定理.结果的特殊情况是多对称多项式代数的有限表示。不变交换方案的约简性被证明是一个副产品。重新讨论了任意基环上的多对称多项式代数。
英文摘要：
First and second fundamental theorems are given for polynomial invariants of a class of pseudo-reflection groups (including the Weyl groups of type $B_n$), under the assumption that the order of the group is invertible in the base field. Special case of the result is a finite presentation of the algebra of multisymmetric polynomials. Reducedness of the invariant commuting scheme is proved as a by-product. The algebra of multisymmetric polynomials over an arbitrary base ring is revisited.
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