Singular Dressing Actions on Harmonic Maps

Extended Solutions of the Harmonic Map Equation in the Special Unitary Group

“…As explained in Remark 2.5 of [5], the bundle W = ΦH n + can be extended holomorphically to M, and, consequently, Φ defines a global extended solution from M to Ω alg G.…”

“…5.5. The cases SU(4) and SU (5). Table 1 shows all the non-trivial canonical elements of SU(4) and SU(5) up to the symmetries χ 1 , χ 2 of Lemma 5.3.…”

“…We have γ ξ 1 = λ −2 π 4 + λ −1 π 3 + λπ 2 + λ 2 π 1 , and, consequently, Table 1. Canonical elements for SU(4) and SU (5).…”

“…However, in general, the symmetric space N χ 2 (ξ) does not coincide with N ξ . For example, in SU(5) the two following situations can occur: for ξ = 5H 1 , we have χ 2 (ξ) = 5H 2 , N ξ = Gr (1,5) and N χ 2 (ξ) = Gr(2, 5); on the other hand, for η = 3H 1 + H 2 + 5H 3 , we have N η = N χ 2 (η) = Gr (2,5).…”

Harmonic maps of finite uniton number into G 2

“…In particular, we show that each harmonic sphere into G 2 can be obtained from a solution of a certain algebraic system of quadratic and cubic equations. 2 The fundamental representation of G 2…”