PreprintCC BY 4.0arXiv
Monodromy Eigenvectors for Difference Equations with Root-of-Unity Step
Abstract
A qKZ-type discrete flat connection with multiplicative step p has monodromy operators when p is a root of unity. The monodromy operators are commuting endomorphisms of the connection. We construct their eigensections and eigenvalues. The construction is based on the presentation of the discrete flat connection as a discrete Gauss-Manin connection.
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BibTeX
@misc{tarasov2026monodromy,
title = {{Monodromy Eigenvectors for Difference Equations with Root-of-Unity Step}},
author = {Vitaly Tarasov and Alexander Varchenko},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.17742},
eprint = {2609.17742},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17742},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Monodromy Eigenvectors for Difference Equations with Root-of-Unity Step
AU - Vitaly Tarasov
AU - Alexander Varchenko
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2609.17742
UR - https://arxiv.org/abs/2609.17742
AB - A qKZ-type discrete flat connection with multiplicative step p has monodromy operators when p is a root of unity. The monodromy operators are commuting endomorphisms of the connection. We construct their eigensections and eigenvalues. The construction is based on the presentation of the discrete flat connection as a discrete Gauss-Manin connection.
ER -