EXPLICIT CONSTRUCTION FOR HARMONIC SURFACES IN U(N) VIA ADDING UNITONS

The authors give an algebraic method to add uniton numbers for harmonic maps from a simply connected domain ? ? R2∪{∞} into the unitary group U(N) with ?nite uniton number. So, it is proved that any n-uniton can be obtained from a 0-uniton by purely algebraic operations and integral transforms to solve the ?ˉ-problem via two different ways.