Ground state representations of some non-rational conformal nets

We construct families of ground state representations of the U (1)-current net and of the Virasoro nets Vir(c) with central charge c >= 1. We show that these representations are not covariant with respect to the original dilations, and those on the U (1)-current net are not solitonic. Furthermore, by going to the dual net with respect to the ground state representations of Virc, one obtains possibly new family of Mobius covariant nets on S-1.