Symmetric Instantons and Skyrme Fields

By explicit construction of the ADHM data, we prove the existence of a charge seven instanton with icosahedral symmetry. By computing the holonomy of this instanton we obtain a Skyrme field which approximates the minimal energy charge seven Skyrmion. We also present a one parameter family of tetrahedrally symmetric instantons whose holonomy gives a family of Skyrme fields which models a Skyrmion scattering process, where seven well-separated Skyrmions collide to form the icosahedrally symmetric Skyrmion.