Koszul duality of affine Kac-Moody algebras and cyclotomic rational DAHA
  We give a proof of the parabolic/singular Koszul duality for the category O of affine Kac-Moody algebras. The main new tool is a relation between moment graphs and finite codimensional affine Schubert varieties. We apply this duality to q-Schur algebras and to cyclotomic rational double affine Hecke algebras. 
Peng Shan (IMJ), Michela Varagnolo (AGM), Eric Vasserot (IMJ)
math.RT