Yang-Mills solutions on de Sitter space of any dimension

For gauge groups SO$(n+1)$, SU$(m+1)$ and Sp$(\mathrm{\ell }+1)$, we construct equivariant Yang-Mills solutions on de Sitter space in $n+1$, $2(m+1)$ and $4(\mathrm{\ell }+1)$ spacetime dimensions. The latter is conformally mapped to a finite cylinder over a coset space realizing an appropriate unit sphere. The equivariance condition reduces the Yang-Mills system to an analog Newtonian particle in one or two dimensions subject to a time-dependent friction and a particular potential. We analyze some properties of the solutions such as their action and energy and display all analytic ones. Beyond dS${}_4$ all such configurations have finite energy but infinite action.