Conical Distributions on the Space of Flat Horocycles - Mathematics > Functional AnalysisReport as inadecuate




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Abstract: Let $G 0=K\ltimes\mathfrak p$ be the Cartan motion group associated with anoncompact semisimple Riemannian symmetric pair $G, K$. Let $\frak a$ be amaximal abelian subspace of $\mathfrak p$ and let $\p=\a+\q$ be thecorresponding orthogonal decomposition. A flat horocycle in $\p$ is a$G 0$-translate of $\q$. A conical distribution on the space $\Xi 0$ of flathorocycles is an eigendistribution of the algebra $\mathbb D\Xi 0$ of$G 0$-invariant differential operators on $\Xi 0$ which is invariant under theleft action of the isotropy subgroup of $G 0$ fixing $\q$. We prove that thespace of conical distributions belonging to each generic eigenspace of $\mathbbD\Xi 0$ is one-dimensional, and we classify the set of all conicaldistributions on $\Xi 0$ when $G-K$ has rank one.



Author: Fulton B. Gonzalez

Source: https://arxiv.org/







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