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Isomonodromic Deformations for Linear q-Difference Systems of Degree One
Abstract
We construct isomonodromy transformations for linear q-difference systems of the form Y(qz)=A(z)Y(z), where A(z)=A0+z A1 has diagonal leading coefficient. These transformations shift eigenvalues of the leading coefficient A1 together with roots of det A(z). They lift compatibility to the right eigenpairs of A(z), yielding a discrete local tau function. The resulting deformation equations preserve the Birkhoff connection matrix, and reduce in their q→ 1 limit to the isomonodromic deformation of a meromorphic connection on ℙ1 with an irregular singularity of Poincaré rank one at ∞.
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BibTeX
@misc{ma2026isomonodromic,
title = {{Isomonodromic Deformations for Linear $q$-Difference Systems of Degree One}},
author = {Yiming Ma},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02952},
eprint = {2609.02952},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02952},
}
RIS
TY - UNPB
TI - Isomonodromic Deformations for Linear q-Difference Systems of Degree One
AU - Yiming Ma
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02952
UR - https://arxiv.org/abs/2609.02952
AB - We construct isomonodromy transformations for linear q-difference systems of the form Y(qz)=A(z)Y(z), where A(z)=A_0+z A_1 has diagonal leading coefficient. These transformations shift eigenvalues of the leading coefficient A_1 together with roots of det A(z). They lift compatibility to the right eigenpairs of A(z), yielding a discrete local tau function. The resulting deformation equations preserve the Birkhoff connection matrix, and reduce in their q→ 1 limit to the isomonodromic deformation of a meromorphic connection on ℙ^1 with an irregular singularity of Poincaré rank one at ∞.
ER -