PreprintCC BY 4.0arXiv
Eigenvectors of p-Curvature for Geometric Difference Equations
Abstract
A qKZ-type additive discrete flat connection in characteristic p has p-curvature operators. They are commuting automorphisms of the connection. We present a Bethe-ansatz-type construction of eigensections and eigenvalues of the p-curvature operators. An eigensection of p-curvature operators is a discrete hypergeometric sum over the finite lattice ℤr/pℤr. Thus, the p-curvature eigensections are constructed by a finite, discrete analogue of a hypergeometric integral.
Related
- Monodromy Eigenvectors for Difference Equations with Root-of-Unity Step
- Eigenvectors and Eigenvalues of p-Curvature Operators for KZ--type Differential Connections
- Geometric difference families and related variable-weight geometric orthogonal codes
- Stability and Periodicity Performance of Solutions of Nonlinear Difference Equations
- Moduli spaces of logarithmic connections associated with difference Painlevé equations of type E(1)n
BibTeX
@misc{tarasov2026eigenvectors,
title = {{Eigenvectors of $p$-Curvature for Geometric Difference Equations}},
author = {Vitaly Tarasov and Alexander Varchenko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.21090},
eprint = {2609.21090},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21090},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Eigenvectors of p-Curvature for Geometric Difference Equations
AU - Vitaly Tarasov
AU - Alexander Varchenko
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2609.21090
UR - https://arxiv.org/abs/2609.21090
AB - A qKZ-type additive discrete flat connection in characteristic p has p-curvature operators. They are commuting automorphisms of the connection. We present a Bethe-ansatz-type construction of eigensections and eigenvalues of the p-curvature operators. An eigensection of p-curvature operators is a discrete hypergeometric sum over the finite lattice ℤ^r/pℤ^r. Thus, the p-curvature eigensections are constructed by a finite, discrete analogue of a hypergeometric integral.
ER -