2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106047Let X be the wonderful compactification of a semisimple adjoint algebraic group. Extending the standard monomials on the flag variety, Chirivi and Maffei constructed a basis of the space of global sections on X that is compatible with all closures of GxG-orbits in X. We show that this basis is also compatible with all BxB-orbit closures by defining subsets using only combinatorics of the underlying paths. Furthermore, we construct standard monomials on X that have properties similar to classical standard monomials.20 pagesRepresentation Theory20G05; 14M17text