Work

Eigenvectors of $p$-Curvature for Geometric Difference Equations

Year: 2026

Type: preprint

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 $\mathbb{Z}^r/p\mathbb{Z}^r$. Thus, the $p$-curvature eigensections are constructed by a finite, discrete analogue of a hypergeometric integral.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.21090

Authors: Tarasov, Vitaly, Varchenko, Alexander

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

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7213945701

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