Splitting fields of characteristic polynomials of random elements in arithmetic groups
Splitting fields of characteristic polynomials of random elements in arithmetic groups
复制标题
算术群中随机元素特征多项式的分裂域
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
D. Zywina
中科院分区：
文献类型：
--
作者：
F. Jouve;Emmanuel Kowalski;D. Zywina
我们讨论而系统的原则，隐含在早期的作品，即为一个“随机”元素的算术子群（分裂，说）约化代数群在数域，分裂领域的特征多项式，计算使用任何faitfhful表示，伽罗瓦群同构的Weyl群的基础代数群。除了我们已经用过的大筛子等工具外，我们引入一些概率的概念，（有限马尔可夫链的大偏差估计）和一般情况下，涉及到更精确的理解的方式Frobenius共轭类计算这样的分裂领域（它与有限Lie型群的正则元与Weyl群中的共轭类之间的映射有关，（卡特和富尔曼早先为其他目的而提出的;我们特别证明了这张地图的值是等分布的）。
We discuss rather systematically the principle, implicit in earlier works, that for a “random” element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the splitting field of the characteristic polynomial, computed using any faitfhful representation, has Galois group isomorphic to the Weyl group of the underlying algebraic group. Besides tools such as the large sieve, which we had already used, we introduce some probabilistic ideas (large deviation estimates for finite Markov chains) and the general case involves a more precise understanding of the way Frobenius conjugacy classes are computed for such splitting fields (which is related to a map between regular elements of a finite group of Lie type and conjugacy classes in the Weyl group which had been considered earlier by Carter and Fulman for other purposes; we show in particular that the values of this map are equidistributed).
影响因子：
1
作者：
Gorodnik A
通讯作者：
Gorodnik A