标题： 超越Cartan分类的随机矩阵 显示英文标题

标题： Random matrices beyond the Cartan classification

摘要： 已知厄米随机矩阵系综可以与李群的对称陪集空间相联系，或者与同一群的切空间相联系。 这导致了随机矩阵系综的分类以及在物理可观测量的实际计算中的应用。 在本文中，我们表明由物理上合理的对称性定义的大量非厄米随机矩阵系综——手征对称性、时间反演不变性、空间旋转不变性、粒子-空穴对称性或不同的实性条件——同样可以与对称空间相联系。 我们给出了与侧代数子空间相联系的随机矩阵系综的显式表示，以及生成不变群的相应对称子代数。 在列出的系综中，我们识别出所有对称空间的卡坦类以及三个具有复特征值的吉尼布雷系综。 显示英文摘要

摘要： It is known that hermitean random matrix ensembles can be identified with symmetric coset spaces of Lie groups, or else with tangent spaces of the same. This results in a classification of random matrix ensembles as well as applications in practical calculations of physical observables. In this paper we show that a large number of non-hermitean random matrix ensembles defined by physically motivated symmetries - chiral symmetry, time reversal invariance, space rotation invariance, particle-hole symmetry, or different reality conditions - can likewise be identified with symmetric spaces. We give explicit representations of the random matrix ensembles identified with lateral algebra subspaces, and of the corresponding symmetric subalgebras spanning the group of invariance. Among the ensembles listed we identify as special cases all the Cartan classes of symmetric spaces and the three Ginibre ensembles with complex eigenvalues.