2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137233In math.RT/0201073 we constructed an equivalence between the derived category of equivariant coherent sheaves on the cotangent bundle to the flag variety of a simple algebraic group and a (quotient of) the category of constructible sheaves on the affine flag variety of the Langlands dual group. Below we prove certain properties of this equivalence; provide a similar ``Langlands dual'' description for the category of equivariant coherent sheaves on the nilpotent cone; and deduce some conjectures by Lusztig and Ostrik.This is a continuation of math.RT/0201073. 13 pages; some correctionsRepresentation TheoryAlgebraic Geometrytext