典型分离不变量
Typical separating invariants
摘要：
证明了一个平凡的极化形式足以产生多项式不变量的分离系统：如果$G$ --$W$和$m$模的直和中的两个点能被多项式不变量分离，则它们能被至多只依赖于$V$型变量的$2\dim(V)$的不变量分离;当$G$是约简的时，仅取决于至多$\dim(V)+1$变量的不变量就足够了。对于有理不变式也有类似的结果。给出了二元多面体群的分离不变量的典型系统中$V$型变量个数的显式界，并将其应用于二元形式的不变量理论。
英文摘要：
It is shown that a trivial version of polarization is sufficient to produce separating systems of polynomial invariants: if two points in the direct sum of the $G$--modules $W$ and $m$ copies of $V$ can be separated by polynomial invariants, then they can be separated by invariants depending only on at most $2\dim(V)$ variables of type $V$; when $G$ is reductive, invariants depending only on at most $\dim(V)+1$ variables suffice. Similar result is valid for rational invariants. Explicit bounds on the number of type $V$ variables in a typical system of separating invariants are given for the binary polyhedral groups, and this is applied to the invariant theory of binary forms.
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