Mackey analogy via D-modules in the example of SL(2,ℝ)

2016/10/13 by Qijun Tan, Tan, Qijun, Yijun Yao +3
Mathematics · #20G05 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1610.04103

openalex publication_date 2016/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 SL(2,ℝ) by considering families of \D-modules over its flag varieties. We make a conjecture which gives a geometric understanding of the Makcey-Higson bijection in the general case.

Related

• Mackey analogy as deformation of D-modules
• How tempered representations of a semisimple Lie group contract to its Cartan motion group
• The algebraic Mackey-Higson bijections
• A Mackey embedding for reduced C*-algebras of real reductive groups
• For a study of definable representations of algebraic groups