Orbital Varieties and Unipotent Representations

Details Orbital Varieties and Unipotent Representations Orbital Varieties and Unipotent Representations

2006-03-29

arxiv.org/abs/math/0603685v2

Mathematics

Representation Theory

35 pages

Scientific paper

Using the notion of a Lagrangian covering, W. Graham and D. Vogan proposed a method of constructing representations from the coadjoint orbits for a complex semisimple Lie group $G$. When the coadjoint orbit $\calO$ is nilpotent, a representation of $G$ is attached to each orbital variety of $\calO$ in this way. In the setting of classical groups, we show that whenever it is possible to carry out the Graham-Vogan construction for an orbital variety of a spherical $\mathcal{O}$, its infinitesimal character lies in a set of characters attached to $\mathcal{O}$ by W. M. McGovern. Furthermore, we show that it is possible to carry out the Graham-Vogan construction for a sufficient number of orbital varieties to account for all the infinitesimal characters in this set.

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