Representations Associated to Small Nilpotent Orbits for Real Spin Groups

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 0 = 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 0 .We consider the nilpotent orbit O c parametrized by [3 2 2k 1 2n-4k-3 ] 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 c transforming according to appropriate characters under C K (O) , and then match them with the K -types of the genuine unipotent representations.The results provide instances for the orbit philosophy.