Cyclotomic double affine Hecke algebras and affine parabolic category O, I

TL;DR

This paper constructs a functor linking affine parabolic category O to cyclotomic rational double affine Hecke algebra category O using orbifold KZ connection, advancing understanding of their relationship.

Contribution

Introduces a functor from affine parabolic category O to cyclotomic rational DAHA category O via orbifold KZ connection, providing new insights into their interplay.

Findings

Establishes a functor connecting the two categories.

Provides several results on the properties of this functor.

Enhances understanding of the relationship between affine parabolic and cyclotomic DAHA categories.

Abstract

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. We give several results concerning this functor.