Conical Distributions on the Space of Flat Horocycles

الأصل · EN

Let G₀=K be the Cartan motion group associated with a noncompact semisimple Riemannian symmetric pair (G, K). Let a be a maximal abelian subspace of p and let =+ be the corresponding orthogonal decomposition. A flat horocycle in is a G₀-translate of. A conical distribution on the space Ξ₀ of flat horocycles is an eigendistribution of the algebra D(Ξ₀) of G₀-invariant differential operators on Ξ₀ which is invariant under the left action of the isotropy subgroup of G₀ fixing. We prove that the space of conical distributions belonging to each generic eigenspace of D(Ξ₀) is one-dimensional, and we classify the set of all conical distributions on Ξ₀ when G/K has rank one.