Higher Orbital Integrals on Motion Groups and Mackey Deformation

2025/07/28 by Román, Angel, Song, Yanli, Tang, Xiang
#FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2507.21008

Abstract

We present an explicit construction of cyclic cocycles on Cartan motion groups, which can be viewed as generalizations of orbital integrals. We show that the higher orbital integral on a real reductive group associated with a semisimple element converges to the corresponding one on the associated Cartan motion group.

Citations

• Cartan Motion Group and Orbital Integrals
• The Mackey bijection for complex reductive groups and continuous fields of reduced group C*-algebras
• How tempered representations of a semisimple Lie group contract to its Cartan motion group

Related

• Cartan Motion Group and Orbital Integrals
• Higher Orbit Integrals, Cyclic Cocyles, and K-theory of Reduced Group C*-algebra
• An index theorem for higher orbital integrals
• A Mackey embedding for reduced C*-algebras of real reductive groups
• Higher orbital integrals, Shalika germs, and the Hochschild homology of Hecke algebras