Conical Distributions on the Space of Flat Horocycles
| dc.creator | Gonzalez, Fulton B. | |
| dc.date | 2009-04-09 | |
| dc.date.accessioned | 2026-07-07T13:01:59Z | |
| dc.date.available | 2026-07-07T13:01:59Z | |
| dc.description | Let $G_0=K\ltimes\mathfrak p$ be the Cartan motion group associated with a noncompact semisimple Riemannian symmetric pair $(G, K)$. Let $\frak a$ be a maximal abelian subspace of $\mathfrak p$ and let $\p=\a+\q$ be the corresponding orthogonal decomposition. A flat horocycle in $\p$ is a $G_0$-translate of $\q$. A conical distribution on the space $Ξ_0$ of flat horocycles is an eigendistribution of the algebra $\mathbb D(Ξ_0)$ of $G_0$-invariant differential operators on $Ξ_0$ which is invariant under the left action of the isotropy subgroup of $G_0$ fixing $\q$. We prove that the space of conical distributions belonging to each generic eigenspace of $\mathbb D(Ξ_0)$ is one-dimensional, and we classify the set of all conical distributions on $Ξ_0$ when $G/K$ has rank one. | |
| dc.identifier | https://arxiv.org/abs/0904.1559 | |
| dc.identifier | http://arxiv.org/abs/0904.1559 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226336 | |
| dc.subject | Functional Analysis | |
| dc.subject | 43A85 | |
| dc.title | Conical Distributions on the Space of Flat Horocycles | |
| dc.type | text |