PreprintCC BY 4.0arXiv
Reducibility of linear representations, free ideals, and Kippenhahn's conjecture
Abstract
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, algebraic extension, spectral index and multiplicity, and characteristic graph. Notably, this framework leads to a complete resolution of Kippenhahn's conjecture by providing necessary and sufficient conditions for its validity.
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BibTeX
@misc{stessin2026reducibility,
title = {{Reducibility of linear representations, free ideals, and Kippenhahn's conjecture}},
author = {Michael Stessin and Rongwei Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.14194},
eprint = {2608.14194},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.14194},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reducibility of linear representations, free ideals, and Kippenhahn's conjecture
AU - Michael Stessin
AU - Rongwei Yang
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2608.14194
UR - https://arxiv.org/abs/2608.14194
AB - 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, algebraic extension, spectral index and multiplicity, and characteristic graph. Notably, this framework leads to a complete resolution of Kippenhahn's conjecture by providing necessary and sufficient conditions for its validity.
ER -