Categorifications and cyclotomic rational double affine Hecke algebras

By Raphaël Rouquier, P. Shan, M. Varagnolo, E. Vasserot. 2013

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Varagnolo and Vasserot conjectured an equivalence between the category $$\mathcal {O}$$O for CRDAHA’s and a subcategory of an affine parabolic category O of type A. We prove this conjecture. As applications, we prove a conjecture of Rouquier on the dimension of simple modules of CRDAHA’s and a conjecture of Chuang–Miyachi on the Koszul duality for the category $$\mathcal {O}$$O of CRDAHA’s.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4dc497b5f823bb77346c76c4c61dfb01d7d8ff4e