2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78167We prove that the global base of the modified quantum algebra of affine GL_N is compatible with the intersection cohomology base of the convolution algebra of the affine flag variety. As a consequence we prove a recent conjecture of Lusztig on the compatibility of the intersection cohomology base with respect to transfer maps.12 pages, AMS-TeXQuantum Algebratext