论文标题
正交稳定性
Orthogonal Stability
论文作者
论文摘要
如果由这些成分的代表固定的所有非二分化二次形式，则称为正交的字符（普通或模块化）。 我们证明这种情况是这种情况，只要没有奇数的正交成分。 我们进一步表明，如果普通特征的还原模式在正交上稳定，则该决定因素是普通型的还原模式。 特别是，如果特征不划分小组顺序，我们立即看到其所在的正交组。 我们绘制用于计算此决定因素的方法，并提供一些示例。
A character (ordinary or modular) is called orthogonally stable if all non-degenerate quadratic forms fixed by representations with those constituents have the same determinant mod squares. We show that this is the case provided there are no odd-degree orthogonal constituents. We further show that if the reduction mod p of an ordinary character is orthogonally stable, this determinant is the reduction mod p of the ordinary one. In particular, if the characteristic does not divide the group order, we immediately see in which orthogonal group it lies. We sketch methods for computing this determinant, and give some examples.
