{
"id": "1712.05552",
"version": "v1",
"published": "2017-12-15T06:15:52.000Z",
"updated": "2017-12-15T06:15:52.000Z",
"title": "Unipotent representations of real classical groups",
"authors": [
"Jia-jun Ma",
"Binyong Sun",
"Chen-Bo Zhu"
],
"categories": [
"math.RT"
],
"abstract": "Let $\\mathbf G$ be a complex orthogonal or complex symplectic group, and let $G$ be a real form of $\\mathbf G$, namely $G$ is a real orthogonal group, a real symplectic group, a quaternionic orthogonal group, or a quaternionic symplectic group. For a fixed parity $\\mathbb p\\in \\mathbb Z/2\\mathbb Z$, we define a set $\\mathrm{Nil}^{\\mathbb p}_{\\mathbf G}(\\mathfrak g)$ of nilpotent $\\mathbf G$-orbits in $\\mathfrak g$ (the Lie algebra of $\\mathbf G$). When $\\mathbb p$ is the parity of the dimension of the standard module of $\\mathbf G$, this is the set of the stably trivial special nilpotent orbits, which includes all rigid special nilpotent orbits. For each $\\mathcal O \\in \\mathrm{Nil}^{\\mathbb p}_{\\mathbf G}(\\mathfrak g)$, we construct all unipotent representations of $G$ (or its metaplectic cover when $G$ is a real symplectic group and $\\mathbb p$ is odd) attached to $\\mathcal O$ via the method of theta lifting and show in particular that they are unitary.",
"revisions": [
{
"version": "v1",
"updated": "2017-12-15T06:15:52.000Z"
}
],
"analyses": {
"subjects": [
"22E45",
"22E46"
],
"keywords": [
"real classical groups",
"unipotent representations",
"real symplectic group",
"stably trivial special nilpotent orbits",
"orthogonal group"
],
"note": {
"typesetting": "TeX",
"pages": 0,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}