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

Abstract

There exists an infinite family of p p -compact groups whose Weyl groups correspond to the finite p p -adic pseudoreflection groups G ( q , r , n ) G(q,r,n) of family 2a in the Clark-Ewing list. In this paper we study these p 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 J -homomorphism. Finally, we also describe a faithful complexification homomorphism from these p p -compact groups to the p p -completion of unitary compact Lie groups.