Work

Eigenvectors and Eigenvalues of $p$-Curvature Operators for KZ--type Differential Connections

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.25269

Authors: Tarasov, Vitaly, Varchenko, Alexander

Institutions: University of North Carolina at Chapel Hill, Indiana University Indianapolis, Indiana University

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214115191

Cites: 8

Cited by:

Related to: 10