Orbital integrals and $K$-theory classes

  title={Orbital integrals and \$K\$-theory classes},
  author={P. Hochs and Hang Wang},
  journal={arXiv: K-Theory and Homology},
  • P. Hochs, Hang Wang
  • Published 2018
  • Mathematics, Physics
  • arXiv: K-Theory and Homology
  • Let $G$ be a semisimple Lie group with discrete series. We use maps $K_0(C^*_rG)\to \mathbb{C}$ defined by orbital integrals to recover group theoretic information about $G$, including information contained in $K$-theory classes not associated to the discrete series. An important tool is a fixed point formula for equivariant indices obtained by the authors in an earlier paper. Applications include a tool to distinguish classes in $K_0(C^*_rG)$, the (known) injectivity of Dirac induction… CONTINUE READING
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