Abstract
The τ-functions introduced by Sato, Miwa, and Jimbo for the deformation theory associated with the Riemann-Hilbert problem on P 1 is shown to be a determinant for a singular Cauchy-Riemann operator whose domain incorporates functions with prescribed branching behavior. The analysis relies heavily on previous work of Malgrange on monodromy preserving deformation theory.
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Palmer, J. Determinants of Cauchy-Riemann operators as τ-functions. Acta Appl Math 18, 199–223 (1990). https://doi.org/10.1007/BF00049126
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DOI: https://doi.org/10.1007/BF00049126