Factorization and symplectic uniton numbers for harmonic maps into symplectic groups |
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| Authors: | HE Qun SHEN Yibing |
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| Affiliation: | 1. Department of Mathematics, West-Brook Campus, Zhejiang University, Hangzhou 310028, China
2. Department of Applied Mathematics, Shanghai Tongji University, Shanghai 200092, China |
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| Abstract: | It is proved that any harmonic map ϕ : Ω →Sp(N) from a simply connected domain Ω ⊆R 2⋃ | ∞ | into the symplectic groupSp(N) ⊂U(2N) with finite uniton number can be factorized into a product of a finite number of symplectic unitons. Based on this factorization, it is proved that the minimal symplectic uniton number of ϕ is not larger thanN, and the minimal uniton number of ϕ is not larger than 2N - 1. The latter has been shown in literature in a quite different way. |
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| Keywords: | harmonic map symplectic group factorization uniton number |
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