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PreprintarXiv licencearXiv

Harmonic sums and the Galois group of the Mellin-KZ difference equation

  • Nikita Markarian
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Abstract

We identify the universal Galois group of the difference equation obtained by the Mellin transform of the Knizhnik-Zamolodchikov equation with the prounipotent group associated with the transport Hopf algebra of Deligne and Terasoma studied in \cite{Markarian}. At each finite weight, we realize the Picard-Vessiot ring by finite multiple harmonic sums. We also interpret the classical Gamma-corrected projected associator as the comparison between finite and regularized asymptotic fibers in this realization.

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Cite

BibTeXRIS
BibTeX
@misc{markarian2026harmonic,
  title = {{Harmonic sums and the Galois group of the Mellin-KZ difference equation}},
  author = {Nikita Markarian},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15463},
  eprint = {2609.15463},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15463},
}
RIS
TY  - UNPB
TI  - Harmonic sums and the Galois group of the Mellin-KZ difference equation
AU  - Nikita Markarian
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15463
UR  - https://arxiv.org/abs/2609.15463
AB  - We identify the universal Galois group of the difference equation obtained by the Mellin transform of the Knizhnik-Zamolodchikov equation with the prounipotent group associated with the transport Hopf algebra of Deligne and Terasoma studied in \cite{Markarian}. At each finite weight, we realize the Picard-Vessiot ring by finite multiple harmonic sums. We also interpret the classical Gamma-corrected projected associator as the comparison between finite and regularized asymptotic fibers in this realization.
ER  -