Title: Gross-Hopkins Duals of Higher Real K-theory Spectra,
Abstract: We determine the Gross-Hopkins duals of certain higher real K-theory spectra.
More specifically, let p be an odd prime, and consider the Morava E-theory
spectrum of height n=p-1. It is known, in the expert circles, that for certain
finite subgroups G of the Morava stabilizer group, the homotopy fixed point
spectra E_n^{hG} are Gross-Hopkins self-dual up to a shift. In this paper, we
determine the shift for those finite subgroups G which contain p-torsion. This
generalizes previous results for n=2 and p=3.