Isomonodromic deformation of resonant rational connections

Details Isomonodromic deformation of resonant rational connections Isomonodromic deformation of resonant rational connections

2005-10-05

arxiv.org/abs/nlin/0510011v1

Int. Math. Res. Papers, (2005), Vol. 2005 Issue 11, Pag. 565-635

Nonlinear Sciences

Exactly Solvable and Integrable Systems

48 pages

Scientific paper

10.1155/IMRP.2005.565

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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