Intersection cohomology of Vinberg-Popov varieties

The Vinberg-Popov variety of a simply connected reductive algebraic group $G$ is a singular affine variety that contains the basic affine space $G\mathrm{/}U$ as a Zariski open subset. It is defined as the spectrum of the ring of functions on $G\mathrm{/}U$, and can also be identified with the universal symplectic implosion for the maximal compact subgroup of $G$. We provide a recursive procedure for computing the intersection cohomology of this variety, with an emphasis on the case where $G={\mathrm{SL}}_n$.