模表示的约化度
Degree of reductivity of a modular representation
摘要：
对于域$F$上的群$G$的有限维表示$V$，约化度$δ(G,V)$是最小度$d$，使得每个非零不动点$v\in V^{G}\setminus\{0\}$可以通过度至多为$d$的齐次不变量与零分离。我们计算$δ(G,V)$明确的几类模群和表示。我们还证明了在模交换$p$ -群的情况下，循环子群的最大尺寸是这个数的一个尖锐的下界。
英文摘要：
For a finite dimensional representation $V$ of a group $G$ over a field $F$, the degree of reductivity $δ(G,V)$ is the smallest degree $d$ such that every nonzero fixed point $v\in V^{G}\setminus\{0\}$ can be separated from zero by a homogeneous invariant of degree at most $d$. We compute $δ(G,V)$ explicitly for several classes of modular groups and representations. We also demonstrate that the maximal size of a cyclic subgroup is a sharp lower bound for this number in the case of modular abelian $p$-groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
