Virasoro Action on Riemann Surfaces, Grassmannians, det \( {\overline \partial _J} \) and Segal-Wilson τ-Function

  • P. G. Grinevich
  • A. Yu. Orlov
Part of the Research Reports in Physics book series (RESREPORTS)


The development of the string theory and the conformal theories on Riemann surfaces results in interest to the objects of the soliton theory (see for example [1]). There is a number of papers using the Segal-Wilson Grassmannians as a model of universal moduli space — the space containing all the Riemann surfaces of finite genus. In the case of superstrings which appears to be simpler the measure was calculated in [2]. Another soliton object — τ-function introduced by the Kyoto mathematicians (see [28], [3] and references therein) may be defined as some vacuum expectation of fermionic fields [4]. Monodromy properties of τ-function [5] were used for calculations of det \( \overline \partial \) for hyperelliptic curves [6].


Vector Field Modulus Space Riemann Surface Meromorphic Function Vertex Operator 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • P. G. Grinevich
    • 1
  • A. Yu. Orlov
    • 2
  1. 1.Landau Institute for Theoretical PhysicsSU-MoscowUSSR
  2. 2.Oceanology InstituteMoscowUSSR

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