  If a geometry $\Gamma$ is isomorphic to the residue of a point $A$ of a
shadow geometry of a spherical building $\Delta$, a representation
$\varepsilon_\Delta^A$ of $\Gamma$ can be given in the unipotent radical
$U_{A^*}$ of the stabilizer in $\mathrm{Aut}(\Delta)$ of a flag $A^*$ of
$\Delta$ opposite to $A$, every element of $\Gamma$ being mapped onto a
suitable subgroup of $U_{A^*}$. We call such a representation a unipotent
representation. We develope some theory for unipotent representations and we
examine a number of interesting cases, where a projective embedding of a Lie
incidence geometry $\Gamma$ can be obtained as a quotient of a suitable
unipotent representation $\varepsilon_\Delta^A$ by factorizing over the derived
subgroup of $U_{A^*}$, while $\varepsilon^A_\Delta$ itself is not a proper
quotient of any other representation of $\Gamma$.
