On the p-compact groups corresponding to the p-adic reflection groups G(q, r, n)

There exists an infinite family of p-compact groupe whose Weyl groups correspond to the finite p-adic peeudoreflection groups G(q, r, n) of family 2a in the Clark-Ewing fist. In this paper we study these p-compact groups. In particular, we construct an analog of the classical Whitney sum map, a family of monomorphisms and a spherical fibration which produces an analog of the classical J-homomorphism. Finally, we also describe a faithful complexification homomorphism from these p-compact groups to the p-completion of unitary compact Lie groups. © 2006 American Mathematical Society.