# Cyclotomic double affine Hecke algebras and affine parabolic category O

@article{Varagnolo2008CyclotomicDA, title={Cyclotomic double affine Hecke algebras and affine parabolic category O}, author={Michela Varagnolo and Eric Vasserot}, journal={Advances in Mathematics}, year={2008}, volume={225}, pages={1523-1588} }

Using the orbifold KZ connection we construct a functor from an affine parabolic category O of type A to the category O of a cyclotomic rational double affine Hecke algebra H. Then we give several results concerning this functor.

## 23 Citations

Heisenberg algebras and rational double affine Hecke algebras

- Mathematics
- 2010

In this paper we categorify the Heisenberg action on the Fock space via the category O of cyclotomic rational double affine Hecke algebras. This permits us to relate the filtration by the support on…

Koszul duality of affine Kac-Moody algebras and cyclotomic rational DAHA

- Mathematics
- 2011

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…

Double a ffi ne Hecke algebras and Hecke algebras associated with quivers

- 2016

This is a short survey of some geometrical and categorical approaches to the representation theory of several algebras related to Hecke algebras, including cyclotomic Hecke algebras, double affine…

KOSZUL DUALITY OF AFFINE KAC -

- 2013

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…

Koszul duality of affine Kac–Moody algebras and cyclotomic rational double affine Hecke algebras

- Mathematics
- 2014

Graded decomposition matrices of v-Schur algebras via Jantzen filtration

- Mathematics
- 2010

We prove that certain parabolic Kazhdan-Lusztig polynomials calculate the graded decomposition matrices of v-Schur algebras given by the Jantzen filtration of Weyl modules, confirming a conjecture of…

Categorifications and cyclotomic rational double affine Hecke algebras

- Mathematics
- 2013

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…

TOWARDS MULTIPLICITIES FOR CATEGORIES O OF CYCLOTOMIC CHEREDNIK ALGEBRAS

- Mathematics
- 2012

Varagnolo and Vasserot conjectured an equivalence between the category O for a cyclotomic Rational Cherednik algebra and a truncation of an affineparabolic category O of type A. In this paper we…

Unitary representations of rational Cherednik algebras, II

- Mathematics
- 2011

The goal of this paper is to classify the unitary irreducible modules in category O for the rational Cherednik algebras of type G(r,1,n). As a first step, we classify those irreducibles in O that are…

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