# Radon transform between affine grassmannians

Let $\overline{GR}(n,k)$ be the manifold of all affine k-dimensional subspaces in $R^n$, and let $R:C^{\infty}_c(\overline{GR}(n,k))\to C^{\infty}_c(\overline{GR}(n,l))$, $0\le k<l\le n-1$, be the Radon transform defined in a standard way as follows: $$(Rf)(E)=\int\limits_{\{L\in \overline{GR}(n,k)):L\subset E\}}f(L)dL.$$ Here the integration is with respect to the Haar measure on $\{L\in \overline{GR}(n,k)):L\subset E\}=\overline{GR}(k,l)$. QUESTION. Is the inversion formula for the Radon transform $R$ known?