Picard groups of higher real K-theory spectra at height p-1

Using the descent spectral sequence for a Galois extension of ring spectra, we compute the Picard group of the higher real K-theory spectra of Hopkins and Miller at height n = p - 1, for p an odd prime. More generally, we determine the Picard groups of the homotopy fixed points spectra E-n(hC), where E-n is Lubin Tate E-theory at the prime p and height n = p - 1, and G is any finite subgroup of the extended Morava stabilizer group. We find that these Picard groups are always cyclic, generated by the suspension.