标题： 特征值分布在幂映射下的图像 显示英文标题

标题： Images of eigenvalue distributions under power maps

摘要： 在[作者的早期工作]中，证明了如果U是一个随机的n×n酉矩阵，那么对于任何p≥n，U^p的特征值是独立同分布的均匀分布；对于一般的紧致李群也得到了类似的结果。 我们研究当p<n时会发生什么。 对于经典群，我们发现可以将U^p的特征值分布用更小的经典群的特征值分布来描述；先前的结果就是这种情况的一个特例。 证明依赖于一个事实，即Weyl群的某个子群本身也是一个Weyl群。 我们推广了这个事实，并利用它来研究一般紧致李群的幂映射问题。 显示英文摘要

摘要： In [earlier work by the author], it was shown that if U is a random n x n unitary matrix, then for any p>=n, the eigenvalues of U^p are i.i.d. uniform; similar results were also shown for general compact Lie groups. We study what happens when p<n instead. For the classical groups, we find that we can describe the eigenvalue distribution of U^p in terms of the eigenvalue distributions of smaller classical groups; the earlier result is then a special case. The proofs rely on the fact that a certain subgroup of the Weyl group is itself a Weyl group. We generalize this fact, and use it to study the power-map problem for general compact Lie groups.