Corpus ID: 203610644

Higher Orbit Integrals, Cyclic Cocyles, and K-theory of Reduced Group C*-algebra

@article{Song2019HigherOI,
  title={Higher Orbit Integrals, Cyclic Cocyles, and K-theory of Reduced Group C*-algebra},
  author={Y. Song and X. Tang},
  journal={arXiv: K-Theory and Homology},
  year={2019}
}
  • Y. Song, X. Tang
  • Published 2019
  • Mathematics
  • arXiv: K-Theory and Homology
  • 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… CONTINUE READING
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