Polytopes, shuffles, quivers and flags
by Professor Arun Ram
Abstract: There are two geometries that show remarkable similarities: that of quiver varieties and that of affine flag varieties. By work of Braverman-Gaitsgory and Gaussent-Littelmann and Kashiwara-Saito and Kamnitzer-Baumann one sees the crystals, in the sense of Kashiwara, coming from both quivers and flags. In the picture of Leclerc-Geiss-Schroer one sees how elements of the shuffle algebra come from quiver varieties. In joint work with A. Ghitza and S. Kannan we are seeing shuffle elements coming from affine flag varieties.
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