Determinants of Cauchy-Riemann operators as \(\tau\)-functions
type: Item
instance of: scholarly article
title: Determinants of Cauchy-Riemann operators as \(\tau\)-functions
zbMATH Open document ID: 0708.35063
DOI: 10.1007/BF00049126
author: John Palmer
published in: Acta Applicandae Mathematicae
publication date: 1990-01-01T00:00:00Z
review text: An interpretation of \(\tau\)-functions [\textit{M. Sato}, \textit{T. Miwa} and \textit{M. Jimbo}, Publ. Res. Inst. Math. Sci., Kyoto Univ. 15, 201-278 (1979; Zbl 0433.35058)] as the determinant of an associated Cauchy- Riemann operator on the spin bundle over \(P_ 1\) is given, based on monodromy preserving deformation theory of Malgrange.
Mathematics Subject Classification ID: 35Q15
Mathematics Subject Classification ID: 35N15
zbMATH DE Number: 4163399
zbMATH Keywords: \(\tau \) -functions
zbMATH Keywords: Cauchy-Riemann operator
zbMATH Keywords: spin bundle
reviewed by: S. K. Rangarajan
MaRDI profile type: Publication
cites work: Q3931657
cites work: Q3756080
cites work: Q4195061
cites work: Painlevé property of monodromy preserving deformation equations and the analyticity of \(\tau\) functions
cites work: Pfaffian bundles and the Ising model
cites work: Q3754832
cites work: Determinants of Cauchy-Riemann operators on a Riemann surface
cites work: Holonomic quantum fields. I
cites work: Loop groups and equations of KdV type
cites work: Notes on infinite determinants of Hilbert space operators
cites work: Quantum field theory, Grassmannians, and algebraic curves
full work available at URL: https://doi.org/10.1007/bf00049126
OpenAlex ID: W1966972849
description: scientific article; zbMATH DE number 4163399