Higher Orbit Integrals, Cyclic Cocyles, and K-theory of Reduced Group C*-algebra
K-Theory and Homology
2019-11-11 v2 Functional Analysis
Operator Algebras
Representation Theory
Abstract
Let G be a connected real reductive group. Orbit integrals define traces on the group algebra of G. We introduce a construction of higher orbit integrals in the direction of higher cyclic cocycles on the Harish-Chandra Schwartz algebra of G. We analyze these higher orbit integrals via Fourier transform by expressing them as integrals on the tempered dual of G. We obtain explicit formulas for the pairing between the higher orbit integrals and the K-theory of the reduced group C*-algebra, and discuss their applications to representation theory and K-theory.
Keywords
Cite
@article{arxiv.1910.00175,
title = {Higher Orbit Integrals, Cyclic Cocyles, and K-theory of Reduced Group C*-algebra},
author = {Yanli Song and Xiang Tang},
journal= {arXiv preprint arXiv:1910.00175},
year = {2019}
}
Comments
41 pages, minor corrections