PreprintCC BY 4.0arXiv
Eigenvectors and Eigenvalues of p-Curvature Operators for KZ--type Differential Connections
Abstract
A KZ-type connection in characteristic p has p-curvature operators. These operators are commuting endomorphisms of the connection. We present a Bethe-ansatz-type construction of their eigenvectors and eigenvalues. The eigenvector is constructed as the value of a characteristic p hypergeometric integral and extends to a flat eigensection over the Frobenius neighborhood of the corresponding Bethe point.
Related
- Two-sample tests for principal eigenvalues and eigenvectors in high-dimensional elliptical factor models
- From Eigenvalues/Eigenvectors of Hypermatrices to Canonical Form of Tensors
- Consequences of Matrices Sharing Eigenvalues and Eigenvectors
- Eigenvectors of p-Curvature for Geometric Difference Equations
- Minimizers of Laplace eigenvalues under a lower curvature bound
BibTeX
@misc{tarasov2026eigenvectors,
title = {{Eigenvectors and Eigenvalues of $p$-Curvature Operators for KZ--type Differential Connections}},
author = {Vitaly Tarasov and Alexander Varchenko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.25269},
eprint = {2609.25269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25269},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Eigenvectors and Eigenvalues of p-Curvature Operators for KZ--type Differential Connections
AU - Vitaly Tarasov
AU - Alexander Varchenko
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2609.25269
UR - https://arxiv.org/abs/2609.25269
AB - A KZ-type connection in characteristic p has p-curvature operators. These operators are commuting endomorphisms of the connection. We present a Bethe-ansatz-type construction of their eigenvectors and eigenvalues. The eigenvector is constructed as the value of a characteristic p hypergeometric integral and extends to a flat eigensection over the Frobenius neighborhood of the corresponding Bethe point.
ER -