Categorifications and cyclotomic rational double affine Hecke algebras. (Q295797)

Varagnolo and Vasserot conjectured an equivalence between the category \(\mathcal O\) for cyclotomic rational double affine Hecke algebras (CRDAHAs) and a subcategory of an affine parabolic category \(\mathcal O\) of type \(A\). In this paper the authors prove this conjecture. As applications, they prove a conjecture of Rouquier on the dimension of simple modules of CRDAHAs and a conjecture of Chuang-Miyachi on the Koszul duality for the category \(\mathcal O\) of CRDAHAs.