论文标题
分开有限场地的不变性
Separating invariants over finite fields
论文作者
论文摘要
我们确定在有限字段$ \ mathbb {f} _q $上，确定了矩阵组$ g <\ mathrm {gl} _n（\ mathbb {f} _q）$的不变环的分离数量的最小数量。我们表明，最小的数字最多可以通过$ | g | n（q-1）$获得。在非模块化的情况下，可以改进这种构建，最多可以为$ n（q-1）$提供不变的学位。作为示例，我们研究了在字段上分离不变的$ \ mathbb {f} _2 $，用于对称组的两个重要表示
We determine the minimal number of separating invariants for the invariant ring of a matrix group $G < \mathrm{GL}_n(\mathbb{F}_q)$ over the finite field $\mathbb{F}_q$. We show that this minimal number can be obtained with invariants of degree at most $|G|n(q-1)$. In the non-modular case this construction can be improved to give invariants of degree at most $n(q-1)$. As examples we study separating invariants over the field $\mathbb{F}_2$ for two important representations of the symmetric group
