线性表示、自由理想的可约性及基普恩哈恩猜想
Reducibility of linear representations, free ideals, and Kippenhahn's conjecture
AI总结：
该研究通过引入极小多项式等关键概念，全面研究矩阵组与有限维群表示的特征多项式，完全解决了矩阵组理论中长期存在的基普恩哈恩猜想。
AI中文摘要：
本文对矩阵组与有限维群表示的特征多项式展开了全面研究，引入了极小多项式、谱指标、谱稳定性及特征图等若干关键概念，该框架完全解决了基普恩哈恩猜想，解决了矩阵组理论中一个长期存在且具影响力的问题。
英文摘要：
This paper presents a comprehensive study of the characteristic polynomial of matrix tuples and finite dimensional group representations. Among other things, several key concepts are introduced, including the minimal polynomial, spectral index, spectral stability, and characteristic graph. Notably, this framework provides a complete resolution to Kippenhahn's conjecture, settling a long-standing and influential problem in the theory of matrix tuples.
