论文标题
反射组的不变差分衍生物的阳性特征
Invariant differential derivations for reflection groups in positive characteristic
论文作者
论文摘要
围绕有限反射群体的许多有趣的命理学源于所罗门著名的1963年定理，描述了不变的差异形式。不变的差分推导还表现出有趣的命理学。当基本领域的特征分割出代理反射群的顺序并且所罗门定理的结论可能失败时，我们尤其是在任意领域上探讨了类似理论。使用Broer和Chuai的结果，我们给出了一个saito标准（雅各布标准），以在有限的群体下找到差异衍生的基础，该基础区分了特征性的特征领域的某些案例。我们表明，反射性增生型在单个轨道中，并在单个轨道上表现出指数和共表达式的跨反向反射词组的双重性。在这种情况下，一组基本派生用于构建具有扭曲楔形的不变差分衍生物的基础。我们获得了特殊线性组SL（N，Q）和一般线性组GL（N，Q）的明确碱基，以及之间的所有组。
Much of the fascinating numerology surrounding finite reflection groups stems from Solomon's celebrated 1963 theorem describing invariant differential forms. Invariant differential derivations also exhibit interesting numerology over the complex numbers. We explore the analogous theory over arbitrary fields, in particular, when the characteristic of the underlying field divides the order of the acting reflection group and the conclusion of Solomon's Theorem may fail. Using results of Broer and Chuai, we give a Saito criterion (Jacobian criterion) for finding a basis of differential derivations invariant under a finite group that distinguishes certain cases over fields of characteristic 2. We show that the reflecting hyperplanes lie in a single orbit and demonstrate a duality of exponents and coexponents when the transvection root spaces of a reflection group are maximal. A set of basic derivations are used to construct a basis of invariant differential derivations with a twisted wedging in this case. We obtain explicit bases for the special linear groups SL(n,q) and general linear groups GL(n,q), and all groups in between.
