Geometric construction of the global base of the quantum modified algebra of affine GL_N

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We 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-TeX

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