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Isomonodromic deformation of resonant rational connections

Marco Bertola·Man Yue Mo
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Abstract

We analyze isomonodromic deformations of rational connections on the Riemann sphere with Fuchsian and irregular singularities. The Fuchsian singularities are allowed to be of arbitrary resonant index; the irregular singularities are also allowed to be resonant in the sense that the leading coefficient matrix at each singularity may have arbitrary Jordan canonical form, with a genericity condition on the Lidskii submatrix of the subleading term. We also give the relevant notion of isomonodromic tau function extending the one of non-resonant deformations introduced by Miwa-Jimbo-Ueno. The tau function is expressed purely in terms of spectral invariants of the matrix of the connection.

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Marco Bertola, Man Yue Mo. 2005-10-05. Isomonodromic deformation of resonant rational connections. https://doi.org/10.1155/imrp.2005.565

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