Langlands functorality in -theory for -algebras. I. Base change

  • Kuok Fai Chao

    Shanghai University, China
  • Hang Wang

    University of Adelaide, Australia and East China Normal University, Shanghai, China

Abstract

We compare representations of the real and complex general linear groups and special linear groups in the framework of -theory, using base change on -parameters. We introduce a notion of base change on -theory involving the fixed point set of the reduced dual of a complex group. For general linear groups, we prove that the base change map is compatible with the Connes–Kasparov isomorphism.

Cite this article

Kuok Fai Chao, Hang Wang, Langlands functorality in -theory for -algebras. I. Base change. J. Noncommut. Geom. 11 (2017), no. 3, pp. 1001–1036

DOI 10.4171/JNCG/11-3-7