Representations associated to small nilpotent orbits for complex Spin groups

Abstract

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 $G_0=Spin(2n,\mathbb{C})$ be the Spin complex group viewed as a real group, and $K\cong G_0$ be the complexification of the maximal compact subgroup of $G_0$. We compute $K$-spectra of the regular functions on some small nilpotent orbits $\mathcal{O}$ transforming according to characters $\psi$ of $C_K(\mathcal{O})$ trivial on the connected component of the identity $C_K(\mathcal{O}{)}^0$. We then match them with the $K$-types of the genuine (i.e. representations which do not factor to $SO(2n,\mathbb{C})$) unipotent representations attached to $\mathcal{O}$.

arXiv admin note: text overlap with arXiv:1702.04841

Cited by in corpus (1)

• Irreducible Characters and Semisimple Coadjoint Orbits