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Moduli spaces of logarithmic connections associated with difference Painlevé equations of type E(1)n

  • Takafumi Matsumoto
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Abstract

In this paper, we provide an explicit correspondence between moduli spaces of parabolic logarithmic connections on the projective line with spectral type (22,14,14) and (32, 23, 16), and the spaces of initial conditions for difference Painlevé equations with symmetry of type E(1)7 and E(1)8, respectively. Furthermore, we realize the extended affine Weyl group symmetries of the space of initial conditions in terms of connections.

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Cite

BibTeXRIS
BibTeX
@misc{matsumoto2026moduli,
  title = {{Moduli spaces of logarithmic connections associated with difference Painlevé equations of type $E^(1)_n$}},
  author = {Takafumi Matsumoto},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29698},
  eprint = {2610.29698},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29698},
}
RIS
TY  - UNPB
TI  - Moduli spaces of logarithmic connections associated with difference Painlevé equations of type E^(1)_n
AU  - Takafumi Matsumoto
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29698
UR  - https://arxiv.org/abs/2610.29698
AB  - In this paper, we provide an explicit correspondence between moduli spaces of parabolic logarithmic connections on the projective line with spectral type (2^2,1^4,1^4) and (3^2, 2^3, 1^6), and the spaces of initial conditions for difference Painlevé equations with symmetry of type E^(1)_7 and E^(1)_8, respectively. Furthermore, we realize the extended affine Weyl group symmetries of the space of initial conditions in terms of connections.
ER  -