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arXiv · 2610.29698

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 $(2^2,1^4,1^4)$ 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.

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Takafumi Matsumoto. 2026-10-21. Moduli spaces of logarithmic connections associated with difference Painlevé equations of type $E^{(1)}_n$. https://arxiv.org/abs/2610.29698

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