101. Special unipotent representations of real classical groups: counting and reduction
- Author
-
Barbasch, Dan, Ma, Jia-Jun, Sun, Binyong, and Zhu, Chen-Bo
- Subjects
Mathematics - Representation Theory ,22E46, 22E47 - Abstract
Let $G$ be a real reductive group in Harish-Chandra's class. We derive some consequences of theory of coherent continuation representations to the counting of irreducible representations of $G$ with a given infinitesimal character and a given bound of the complex associated variety. When $G$ is a real classical group (including the real metaplectic group), we investigate the set of special unipotent representations of $G$ attached to $\check{\mathcal O}$, in the sense of Arthur and Barbasch-Vogan. Here $\check{\mathcal O}$ is a nilpotent adjoint orbit in the Langlands dual of $G$ (or the metaplectic dual of $G$ when $G$ is a real metaplectic group). We give a precise count for the number of special unipotent representations of $G$ attached to $\check{ \mathcal O}$. We also reduce the problem of constructing special unipotent representations attached to $\check{\mathcal O}$ to the case when $\check{\mathcal O}$ is analytically even (equivalently for a real classical group, has good parity in the sense of M{\oe}glin). The paper is the first in a series of two papers on the classification of special unipotent representations of real classical groups.
- Published
- 2022