标题： 随机矩阵超出卡坦分类 显示英文标题

标题： Random matrices beyond the Cartan classification

摘要： 已知厄米特随机矩阵系综可以被识别为李群的对称陪集空间，或者与相同的李群的切空间相对应。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。 本文中我们展示了由物理激发的对称性定义的大类非厄米特随机矩阵系综——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部条件——同样可以被识别为对称空间。 我们给出了与侧向代数子空间相对应的随机矩阵系综的具体表示形式，以及对应对称子代数张成的不变性群。 在列出的系综中，我们确定了所有与对称空间的卡坦类相对应的厄米特系综以及具有复特征值的三个吉尼布系综作为特殊情况。 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 hermitean ensembles identified with Cartan classes of symmetric spaces and the three Ginibre ensembles with complex eigenvalues.