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An index theorem for higher orbital integrals

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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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Acknowledgements

Hochs is partially supported by Discovery Project DP200100729 from the Australian Research Council; Song is partially supported by NSF Grant DMS-1800667; Tang is partially supported by NSF Grants DMS-1363250 and DMS-1800666.

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Authors and Affiliations

  1. Radboud University, Heyendaalseweg 135, 6525, AJ Nijmegen, The Netherlands

    Peter Hochs

  2. Washington University in St. Louis, St. Louis, MO, USA

    Yanli Song & Xiang Tang

Authors
  1. Peter Hochs
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  2. Yanli Song
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  3. Xiang Tang
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Correspondence to Yanli Song.

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Communicated by Thomas Schick.

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Hochs, P., Song, Y. & Tang, X. An index theorem for higher orbital integrals. Math. Ann. 382, 169–202 (2022). https://doi.org/10.1007/s00208-021-02233-3

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