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Unitarization of Loop Group Representations of Fundamental Groups

Published online by Cambridge University Press:  11 January 2016

Josef Dorfmeister  and
Hongyou Wu
Josef Dorfmeister
Affiliation:
Department of Mathematics, Tech University of Munich, Garching D-85747, Germany
Hongyou Wu
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA
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Abstract

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In this paper, we give a characterization of the simultaneous unitarizability of any finite set of SL(2, ℂ)-valued functions on and determine all possible ways of the unitarization. Such matrix functions can be regarded as images of the generators for the fundamental group of a surface in an -family, and the results of this paper have applications in the construction of constant mean curvature surfaces in space.

Keywords

22E6753A1053C42
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 187 , September 2007 , pp. 1 - 33
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2007

References

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