Representations associated to small nilpotent orbits for complex Spin groups

This paper provides a comparison between the K-structure of unipotent representations and regular sections of bundles on nilpotent orbits for complex groups of type D. Precisely, let G₀ = Spin(2n,c[double-struck]) be the Spin complex group as a real group, and let K ≅ G₀ be the complexification of the maximal compact subgroup of G₀. We compute K-spectra of the regular functions on some small nilpotent orbits O transforming according to characters ψ of C_K(O) trivial on the connected component of the identity C_K(O)⁰. We then match them with the K-types of the genuine (i.e., representations which do not factor to SO(2n,c[double-struck])) unipotent representations attached to O.