Mackey analogy as deformation of D-modules

2017/07/02 by Yu, Shilin · 1 citation
#14F10 #22E46 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1707.00240

Abstract

Given a real reductive group Lie group G_ℝ, the Mackey analogy is a bijection between the set of irreducible tempered representations of G_ℝ and the set of irreducible unitary representations of its Cartan motion group. We show that this bijection arises naturally from families of twisted D-modules over the flag variety of G_ℝ.

Cited by

• Dirac operators for algebraic families

Related

• Mackey analogy via D-modules in the example of SL(2,ℝ)
• How tempered representations of a semisimple Lie group contract to its Cartan motion group
• A Mackey embedding for reduced C*-algebras of real reductive groups
• The Mackey bijection for complex reductive groups and continuous fields of reduced group C*-algebras
• A Derived Decomposition for Equivariant D-modules