An index theorem for higher orbital integrals
Differential Geometry
2021-06-30 v2 K-Theory and Homology
Operator Algebras
Representation Theory
Abstract
Recently, two of the authors of this paper constructed cyclic cocycles on Harish-Chandra's Schwartz algebra of linear reductive Lie groups that detect all information in the -theory of the corresponding group -algebra. The main result in this paper is an index formula for the pairings of these cocycles with equivariant indices of elliptic operators for proper, cocompact actions. This index formula completely determines such equivariant indices via topological expressions.
Keywords
Cite
@article{arxiv.2005.06119,
title = {An index theorem for higher orbital integrals},
author = {Peter Hochs and Yanli Song and Xiang Tang},
journal= {arXiv preprint arXiv:2005.06119},
year = {2021}
}
Comments
40 pages; updates based on referee comments; expanded proof of Proposition 3.3