Journal of Lie Theory

no. 3
Irreducible Characters and Semisimple Coadjoint Orbits
Journal of Lie Theory, Volume 30 (2020) no. 3, pp. 715-765
When $G_{\mathbb{R}}$ is a real, linear algebraic group, the orbit method predicts that nearly all of the unitary dual of $G_{\mathbb{R}}$ consists of representations naturally associated to orbital parameters $(\mathcal{O},\Gamma)$. If $G_{\mathbb{R}}$ is a real, reductive group and $\mathcal{O}$ is a semisimple coadjoint orbit, the corresponding unitary representation $\pi(\mathcal{O}, \Gamma)$ may be constructed utilizing Vogan and Zuckerman's cohomological induction together with Mackey's real parabolic induction. In this article, we give a geometric character formula for such representations $\pi(\mathcal{O},\Gamma)$. Special cases of this formula were previously obtained by Harish-Chandra and Kirillov when $G_{\mathbb{R}}$ is compact and by Rossmann and Duflo when $\pi(\mathcal{O},\Gamma)$ is tempered.
DOI: 10.5802/jolt.1137
Classification: 22E46
Keywords: Semisimple orbit, coadjoint orbit, orbit method, Kirillov's character formula, cohomological induction, parabolic induction, reductive group 
@article{JOLT_2020_30_3_a6,
     author = {B. Harris and Y. Oshima},
     title = {Irreducible {Characters} and {Semisimple} {Coadjoint} {Orbits}},
     journal = {Journal of Lie Theory},
     pages = {715--765},
     year = {2020},
     volume = {30},
     number = {3},
     doi = {10.5802/jolt.1137},
     zbl = {1478.22011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1137/}
}
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B. Harris; Y. Oshima. Irreducible Characters and Semisimple Coadjoint Orbits. Journal of Lie Theory, Volume 30 (2020) no. 3, pp. 715-765. doi: 10.5802/jolt.1137

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