JournalsjncgVol. 11, No. 3pp. 1001–1036

Langlands functorality in KK-theory for CC^*-algebras. I. Base change

  • Kuok Fai Chao

    Shanghai University, China
  • Hang Wang

    University of Adelaide, Australia and East China Normal University, Shanghai, China
Langlands functorality in $K$-theory for $C^*$-algebras. I. Base change cover
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Abstract

We compare representations of the real and complex general linear groups and special linear groups in the framework of KK-theory, using base change on LL-parameters. We introduce a notion of base change on KK-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 KK-theory for CC^*-algebras. I. Base change. J. Noncommut. Geom. 11 (2017), no. 3, pp. 1001–1036

DOI 10.4171/JNCG/11-3-7