2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118143Using Ram's theory of alcove walks, we give a proof of the Bernstein presentation of the affine Hecke algebra. The method works also in the case of unequal parameters. We also discuss how these results help in studying sheaves of nearby cycles on affine flag manifolds.Representation TheoryAlgebraic Geometry20C08text