Nagoya Mathematical Journal

Unitarization of loop group representations of fundamental groups

Josef Dorfmeister and Hongyou Wu

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Abstract

In this paper, we give a characterization of the simultaneous unitarizability of any finite set of $\operatorname{SL}(2, \mathbb{C})$-valued functions on $\mathbb{S}^{1}$ 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 $\mathbb{S}^{1}$-family, and the results of this paper have applications in the construction of constant mean curvature surfaces in space.

Article information

Source
Nagoya Math. J., Volume 187 (2007), 1-33.

Dates
First available in Project Euclid: 4 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1188913892

Mathematical Reviews number (MathSciNet)
MR2354553

Zentralblatt MATH identifier
1135.22020

Subjects
Primary: 22E67: Loop groups and related constructions, group-theoretic treatment [See also 58D05]
Secondary: 53A10: Minimal surfaces, surfaces with prescribed mean curvature [See also 49Q05, 49Q10, 53C42] 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42]

Citation

Dorfmeister, Josef; Wu, Hongyou. Unitarization of loop group representations of fundamental groups. Nagoya Math. J. 187 (2007), 1--33. https://projecteuclid.org/euclid.nmj/1188913892


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