Representations associated to small nilpotent orbits for complex Spin groups

2017/02/27 by Barbasch, Dan, Tsai, Wan-Yu
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1702.08223

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≅ G₀ be the complexification of the maximal compact subgroup of G₀. We compute K-spectra of the regular functions on some small nilpotent orbits \mathcal O transforming according to characters ψ 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.

Related

• Representations associated to small nilpotent orbits for real Spin groups
• Genuine special unipotent representations of spin groups
• Regular functions on covers of nilpotent coadjoint orbits
• Unipotent representations and the dual pair correspondence
• Unipotent Representations Attached to the Principal Nilpotent Orbit