New York Journal of Mathematics
Volume 27 (2021), 253-271


David Radnell, Eric Schippers, Mohammad Shirazi, and Wolfgang Staubach

Schiffer operators and calculation of a determinant line in conformal field theory

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Published: January 25, 2021.
Keywords: rigged Riemann surfaces, determinant line, two-dimensional conformal field theory.
Subject: 30C40, 30F99, 58J52, 58Z05, 81T40.

We consider an operator associated to compact Riemann surfaces endowed with a conformal map, f, from the unit disk into the surface, which arises in conformal field theory. This operator projects holomorphic functions on the surface minus the image of the conformal map onto the set of functions h so that the Fourier series h ∘ f has only negative powers. We give an explicit characterization of the cokernel, kernel, and determinant line of this operator in terms of natural operators in function theory.


D. Radnell acknowledges the support of the Academy of Finland's project "Algebraic structures and random geometry of stochastic lattice model".

Author information

David Radnell:
Department of Mathematics and Systems Analysis
Aalto University
P.O. Box 11100, FI-00076 Aalto, Finland


Eric Schippers:
Department of Mathematics and Statistics
University of Manitoba
Winnipeg, MB R3T 2N2, Canada


Mohammad Shirazi:
Department of Mathematics and Statistics
McGill University
Montreal, QC H3A 0B9, Canada


Wolfgang Staubach:
Department of Mathematics
Uppsala University
S-751 06 Uppsala, Sweden