Abstract
The results in this paper provide a comparison between the K-structure of unipotent representations and regular sections of bundles on nilpotent orbits. Precisely, let G <sub>0</sub> = Spin (a,b) with a + b = 2n, the nonlinear double cover of Spin(a,b), and let K = Spin(a,C) × Spin(b,C) be the complexification of the maximal compact subgroup of G <sub>0</sub> . We consider the nilpotent orbit O <sub>c</sub> parametrized by [3 2 <sup>2k</sup> 1 <sup>2</sup> n <sup>−</sup> <sup>4k−3</sup> ] with k > 0. We provide a list of unipotent representations that are genuine, and prove that the list is complete using the coherent continuation representation. Separately we compute K -spectra of the regular functions on certain real forms O of O <sub>c</sub> transforming according to appropriate characters ψ under C <sub>K</sub> (O), and then match them with the K -types of the genuine unipotent representations. The results provide instances for the orbit philosophy.