2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/145520Let g be a complex semisimple Lie algebra and let G' be the Langlands dual group. We give a description of the cohomology algebra of an arbitrary spherical Schubert variety in the loop Grassmannian for G' as a quotient of the form Sym(g^e)/J. Here, J is an appropriate ideal in the symmetric algebra of g^e, the centralizer of a principal nilpotent in g. We also discuss a `topological' proof of Kostant's famous result on the structure of the polynomial algebra on g.Final version to appear in a special volume dedicated to Bertram Kostant. It supercedes arXiv:math.AG/9803141Representation TheoryAlgebraic Geometrytext