论文标题
特征两个和正常子组中的自偶联模块
Self-dual modules in characteristic two and normal subgroups
论文作者
论文摘要
我们证明了Clifford的理论结果在有限群体的表示形式上，这些群体的特征$ 2 $。 令$ g $为有限的组，让$ n $为$ g $的普通亚组，让$φ$是自dual $ n $的不可约2 $ 2 $ brauer的角色。我们证明，$ g $的唯一自我偶然不可约的brauer字符$θ$ $ g $，因此$φ$在$θ$ to $ n $的限制下出现了奇数。此外，这种多重性是$ 1 $。 相反，如果$θ$是$ g $的$ 2 $ 2 $ brauer字符，$ g $是自dual类型但不是二次类型的，则限制$θ$对$ n $的限制是$ n $的独特自我偶尔不可约束的brauer字符，而没有Quadratic类型。 让$ b $为$ n $的真正2 $ block。我们表明，覆盖$ b $的$ g $有一个独特的$ 2 $块，这很弱。
We prove Clifford theoretic results on the representations of finite groups which only hold in characteristic $2$. Let $G$ be a finite group, let $N$ be a normal subgroup of $G$ and let $φ$ be an irreducible $2$-Brauer character of $N$ which is self-dual. We prove that there is a unique self-dual irreducible Brauer character $θ$ of $G$ such that $φ$ occurs with odd multiplicity in the restriction of $θ$ to $N$. Moreover this multiplicity is $1$. Conversely if $θ$ is an irreducible $2$-Brauer character of $G$ which is self-dual but not of quadratic type, the restriction of $θ$ to $N$ is a sum of distinct self-dual irreducible Brauer character of $N$, none of which have quadratic type. Let $b$ be a real $2$-block of $N$. We show that there is a unique real $2$-block of $G$ covering $b$ which is weakly regular.
