2001•Chinese Annals of Mathematics Series BRequires access

ON HARMONIC MAPS INTO SYMPLECTIC GROUPS Sp(N)

Qun He, Yibing Shen

Abstract

By means of the theory of harmonic maps into the unitary group U(N), the authors study harmonic maps into the symplectic group Sp(N). The symplectic uniton and symplectic extended uniton are introduced. The method of the symplectic Bäcklund transformation and the Darboux transformation is used to construct new symplectic unitons from a known one.

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Key concepts: Symplectic geometry, Symplectic representation, Symplectic group, Moment map, Symplectomorphism, Symplectic matrix, Mathematics, Unitary state