标题： 杜伊斯塔马特三重指标和厄米矩阵的差 显示英文标题

标题： Duistarmaat's triple index and the difference of Hermitian matrices

摘要： 在本文中，我们开发了一种系统的方法学，用于杜斯特马特指标，这是一个为拉格朗日子空间三元组定义的辛不变量。 近半个世纪前引入的这个指标，由于其在量子图上的本征值交错问题（以及更抽象地对于对称算子的自伴扩张）中的核心作用，最近再次引起了关注。 在这里，我们给出了该指标的公理化特征，这导致了其基本性质的简单证明。 我们还将该指标与其他在辛几何中经常出现的量相关联，例如霍尔曼-芦屋-沃尔指数和莫尔斯指数。 其中一些联系导致了一个关于厄米特矩阵差的莫尔斯指数的有趣公式。 显示英文摘要

摘要： In this paper we develop a systematic calculus for the Duistermaat index, a symplectic invariant defined for triples of Lagrangian subspaces. Introduced nearly half a century ago, this index has lately been the subject of renewed attention, due to its central role in eigenvalue interlacing problems on quantum graphs (and more abstractly for self-adjoint extensions of symmetric operators). Here we give an axiomatic characterization of the index that leads to elementary proofs of its fundamental properties. We also relate the index to other quantities often appearing in symplectic geometry, such as the H\"ormander--Kashiwara--Wall index and the Maslov index. Among other things, this leads to a curious formula for the Morse index of a difference of Hermitian matrices.