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Abstract: H-instantons are a distinguished type of connections on Riemannian n-manifolds, as they are generalizations of anti-self-dual connections to dimensions n geq 4. Examples of H-instantons include primitive Hermitian Yang-Mills (pHYM) connections, Spin(7)-instantons, which have been of great interest in the recent years, and the less studied Sp(n)-instantons.

In this talk, we describe Sp(2)-instantons on hyperkähler eight-manifolds and their relations with other gauge-theoretical objects. We then construct examples of Sp(2)-instantons, pHYM connections and Spin(7) instantons with symmetry on the manifold T^*CP^2 with the Calabi hyperkähler structure.