有限群作用的压缩和协变维数，II
Compression of Finite Group Actions and Covariant Dimension, II
摘要：
设$G$是有限群，$ϕ: V\to W$是有限维$G$ -模的等变态射.如果$G$忠实地作用于$ϕ(V)$，我们说$ϕ$是忠实的。$G$的协变维数是在所有忠实的$ϕ$上取的$\bar{ϕ(V)}$的维数的最小值。在\cite{KS07}中，我们研究了协变维数，并能够在许多情况下确定它。我们的技术在很大程度上依赖于找到同质的忠实协变量。在\cite{KS07}发表后，本文的初级作者指出了我们证明中的几个缺陷。幸运的是，这启发了我们找到更好的技术，涉及多齐次协变，这使我们能够扩展和完成的结果，简化证明和填补\cite{KS07}的空白。
英文摘要：
Let $G$ be a finite group and $ϕ: V\to W$ an equivariant morphism of finite dimensional $G$-modules. We say that $ϕ$ is faithful if $G$ acts faithfully on $ϕ(V)$. The covariant dimension of $G$ is the minimum of the dimension of $\bar{ϕ(V)}$ taken over all faithful $ϕ$. In \cite{KS07} we investigated covariant dimension and were able to determine it in many cases. Our techniques largely depended upon finding homogeneous faithful covariants. After publication of \cite{KS07}, the junior author of this article pointed out several gaps in our proofs. Fortunately, this inspired us to find better techniques, involving multihomogeneous covariants, which have enabled us to extend and complete the results, simplify the proofs and fill the gaps of \cite{KS07}.
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