We show that the conformally invariant fractional powers of the sub-Laplacian
on the Heisenberg group are given in terms of the scattering operator for an
extension problem to the Siegel upper halfspace. Remarkably, this extension
problem is different from the one studied, among others, by Caffarelli and
Silvestre.Comment: 33 pages. arXiv admin note: text overlap with arXiv:0709.1103 by
other author
