AbstractIn this talk we introduce a hybrid quantum group at root of unity. We consider its category O and discuss some basic properties including linkage principle and BGG reciprocity. Then we show that there is an isomorphism between the center of a block (of arbitrary singular type) of the category O with the cohomology ring of the partial affine flag variety (of the corresponding parahoric t...
Abstract:A subgraph of an edge-coloured graph is called rainbow if all its edges have distinct colours. The study of rainbow subgraphs has a long history in discrete mathematics, going back to the 18th century work of Euler on Latin squares. Since then rainbow structures were the focus of extensive research and found numerous applications in design theory and graph decompositions. Many problem...