The Dependence on the Monodromy Data of the Isomonodromic Tau Function

  title={The Dependence on the Monodromy Data of the Isomonodromic Tau Function},
  author={Marco Bertola},
  journal={Communications in Mathematical Physics},
  • M. Bertola
  • Published 26 February 2009
  • Mathematics
  • Communications in Mathematical Physics
The isomonodromic tau function defined by Jimbo-Miwa-Ueno vanishes on the Malgrange’s divisor of generalized monodromy data for which a vector bundle is nontrivial, or, which is the same, a certain Riemann–Hilbert problem has no solution. In their original work, Jimbo, Miwa, Ueno provided an algebraic construction of its derivatives with respect to isomonodromic times. However the dependence on the (generalized) monodromy data (i.e. monodromy representation and Stokes’ parameters) was not… 

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