Higher Orbital Integrals on Motion Groups and Mackey Deformation

TL;DR

This paper constructs explicit cyclic cocycles on Cartan motion groups, generalizing orbital integrals, and demonstrates their convergence from real reductive groups to associated motion groups.

Contribution

It provides a new explicit construction of cyclic cocycles on Cartan motion groups and establishes their convergence from higher orbital integrals on real reductive groups.

Findings

Explicit cyclic cocycles constructed on Cartan motion groups

Higher orbital integrals converge from real reductive groups to motion groups

Generalization of orbital integrals to a broader class of groups

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.