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arXiv · 2005.06119

An index theorem for higher orbital integrals

Peter Hochs·Yanli Song·Xiang Tang
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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 $K$-theory of the corresponding group $C^*$-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.

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Peter Hochs, Yanli Song, Xiang Tang. 2020-05-13. An index theorem for higher orbital integrals. https://arxiv.org/abs/2005.06119

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