# Cyclotomic double affine Hecke algebras

@article{Alexander2020CyclotomicDA, title={Cyclotomic double affine Hecke algebras}, author={Braverman Alexander and V Finkelberg Mikhail and Etingof Pavel}, journal={Annales Scientifiques De L Ecole Normale Superieure}, year={2020}, volume={53}, pages={1249-1312} }

We show that the partially spherical cyclotomic rational Cherednik algebra (obtained from the full rational Cherednik algebra by averaging out the cyclotomic part of the underlying reflection group) has four other descriptions: (1) as a subalgebra of the degenerate DAHA of type A given by generators; (2) as an algebra given by generators and relations; (3) as an algebra of differential-reflection operators preserving some spaces of functions; (4) as equivariant Borel-Moore homology of a certain…

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