On the kernel of the maximal flat Radon transform on symmetric spaces of compact type

Abstract

Let $M$ be a Riemannian globally symmetric space of compact type, $M^{\prime }$ its set of maximal flat totally geodesic tori, and $\mathrm{ad}(M)$ its adjoint space. We show that the kernel of the maximal flat Radon transform $\tau :L^2(M)\to L^2(M^{\prime })$ is precisely the orthogonal complement of the image of the pullback map $L^2(\mathrm{ad}(M))\to L^2(M)$. In particular, we show that the maximal flat Radon transform is injective if and only if $M$ coincides with its adjoint space.

13 pages; corrected typographical errors; revised argument in section 4; results unchanged

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