Special Unipotent Representations with Half Integral Infinitesimal Characters

Abstract

For any special nilpotent orbit, let $\frac{1}{2}{h}^{\vee }$ be one half of the semisimple element of a Jacobson-Morozov triple associated to the orbit. In 1985, Barbasch and Vogan defined the notion of special unipotent representations with infinitesimal character $(\frac{1}{2}{h}^{\vee },\frac{1}{2}{h}^{\vee })$. Some properties of such representations were discovered when $\frac{1}{2}{h}^{\vee }$ is integral. In this manuscript, we give a complete proof of these properties when $\frac{1}{2}{h}^{\vee }$ is not integral.

this work is now in the Appendix of arXiv:1706.02510

References in corpus (1)

• Induce/restrict matrices for exceptional Weyl groups