Actions of loop groups on harmonic maps

M. J. Bergvel, M. A. Guest

研究成果: Article査読

25 被引用数 (Scopus)

抄録

We describe a general framework in which subgroups of the loop group AGlnC act on the space of harmonic maps from S2 to GlnC. This represents a simplification of the action considered by Zakharov-Mikhailov-Shabat [ZM, ZS] in that we take the contour for the Riemann-Hilbert problem to be a union of circles; however, it reduces the basic ingredient to the well-known Birkhoff decomposition of AGlnnC, and this facilitates a rigorous treatment. We give various concrete examples of the action, and use these to investigate a suggestion of Uhlenbeck [Uh] that a limiting version of such an action (“completion”) gives rise to her fundamental process of “adding a uniton”. It turns out that this does not occur, because completion preserves the energy of harmonic maps. However, in the special case of harmonic maps from S2 to complex projective space, we describe a modification of this completion procedure which does indeed reproduce “adding a uniton”.

本文言語English
ページ(範囲)861-886
ページ数26
ジャーナルTransactions of the American Mathematical Society
326
2
DOI
出版ステータスPublished - 1991 8
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)
  • 応用数学

フィンガープリント

「Actions of loop groups on harmonic maps」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル