Mackey analogy via 𝒟-modules for SL(2, ℝ)

A conjecture by Mackey and Higson claims that there is close relationship between irreducible representations of a real reductive group and those of its Cartan motion group. The case of irreducible tempered unitary representations has been verified recently by Afgoustidis. We study the admissible representations of [Formula: see text] by considering families of [Formula: see text]-modules over its flag varieties. We make a conjecture which gives a geometric understanding of the Makecy–Higson bijection in the general case.