Parabolic induction and restriction functors for rational Cherednik algebras

Abstract

Parabolic induction and restriction functors play an important role in the representation theory of finite and affine Hecke algebras. This makes it desirable to generalize them to the setting of double affine Hecke algebras, or Cherednik algebras. However, a naive attempt to do so fails: the definition of parabolic induction and restriction functors for finite and affine Hecke algebras uses the fact that the Hecke algebra attached to a parabolic subgroup can be embedded into the Hecke algebra attached to the whole group, which is not the case in the double affine setting.