Intersection Cohomology of Popov–Vinberg Varieties

The Popov–Vinberg variety of a simply connected, split, semisimple algebraic group G is a singular affine variety that contains the basic affine space G / U as a Zariski open subset. It is defined as the spectrum of the ring of functions on G / 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 = SLₙ G = SL n .