发表机构
Universidad Politécnica de Madrid（马德里理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文描述固定非简单谱的三对角对称实矩阵等谱集的拓扑，证明其为无环空间且贝蒂数为组合数，并推广至分裂实半单李代数。
AI 中文摘要
我们描述了具有固定非简单谱的三对角对称实矩阵集合的拓扑。三对角等谱集不是相应正交共轭类的子流形，而是若干子流形的集合，这些子流形清洁相交。我们证明三对角等谱集是一个无环空间，且其贝蒂数为组合数。这推广了已知对简单谱成立的构造和结果到任意谱情形。我们还将这些结果推广到分裂实半单李代数。
英文摘要
We describe the topology of the set of tridiagonal symmetric real matrices with fixed non-simple spectrum. The tridiagonal isospectral set is not a submanifold of the corresponding orthogonal conjugacy class, but a collection of submanifolds which intersect cleanly. We show that the tridiagonal isospectral set is an aspherical space and that its Betti numbers are combinatorial numbers. This generalizes to arbitrary spectrum constructions and results known for simple spectrum. We also extend these results to split real semisimple Lie algebras.
