10,741 research outputs found
Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras
We define the i-restriction and i-induction functors on the category O of the
cyclotomic rational double affine Hecke algebras. This yields a crystal on the
set of isomorphism classes of simple modules, which is isomorphic to the
crystal of a Fock space.Comment: 31 page
Canonical bases and affine Hecke algebras of type D
We prove a conjecture of Kashiwara and Miemietz on canonical bases and
branching rules of affine Hecke algebras of type D. The proof is similar to the
proof of the type B case.Comment: 24 page
Categorifications and cyclotomic rational double affine Hecke algebras
Varagnolo and Vasserot conjectured an equivalence between the category 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 O of CRDAHA's.Comment: 85 page
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