一般线性群的共轭实类
Conjugate Real Classes in General Linear Groups
摘要：
设$\F$是具有非平凡对合$c: α\to α^c$的域。如果元素$g \in {\rm GL}_n(\F)$与$(g^c)^{-1}$共轭，则称为$c$ -实数。证明了对$n \geq 2$，$g \in {\rm GL}_n(\F)$是$c$ -实的当且仅当它在$\F$上的某个次数为$n$的酉群中有表示.
英文摘要：
Let $\F$ be a field with a non-trivial involution $c: α\to α^c$. An element $g \in {\rm GL}_n(\F)$ is called $c$-real if it is conjugate to $(g^c)^{-1}$. We prove that for $n \geq 2$, $g \in {\rm GL}_n(\F)$ is $c$-real if and only if it has a representation in some unitary group of degree $n$ over $\F$.
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