论文标题
有限简单正交组的一些现实特性
Some Reality Properties of Finite Simple Orthogonal Groups
论文作者
论文摘要
我们证明了有限简单正交组的几种现实属性。对于任何主要功率$ q $和$ m \ geq 1 $，我们证明所有真正的共轭类在简单的组中都是强烈的，$ \ mathrm {p}ω^{\ pm}（\ pm}（\ pm}（4m+2，q），m \ geq 1 $，m \ geq 1 $，除了情况下3（\ mathrm {mod} \; 4）$，我们在此特殊情况下为任何$ m $构建了弱真实的类。我们还表明，没有$ \ mathrm {p}ω^{\ pm}（n，q）$具有frobenius-schur指示器$ -1 $的不可约的复杂性，除非在情况下可能是$ \ mathrm {p}Ω
We prove several reality properties for finite simple orthogonal groups. For any prime power $q$ and $m\geq 1$, we show that all real conjugacy classes are strongly real in the simple groups $\mathrm{P}Ω^{\pm}(4m+2,q), m \geq 1$, except in the case $\mathrm{P}Ω^{-}(4m+2,q)$ with $q \equiv 3(\mathrm{mod} \; 4)$, and we construct weakly real classes in this exceptional case for any $m$. We also show that no irreducible complex character of $\mathrm{P}Ω^{\pm}(n,q)$ can have Frobenius-Schur indicator $-1$, except possibly in the case $\mathrm{P}Ω^{-}(4m+2,q)$ with $q \equiv 3(\mathrm{mod} \; 4)$.
