Langlands functorality in $K$-theory for $C^*$-algebras. I. Base change

Kuok Fai Chao; Hang Wang

doi:10.4171/jncg/11-3-7

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

Langlands functorality in $K$ -theory for $C^{*}$ -algebras. I. Base change

Kuok Fai Chao
Shanghai University, China
Hang Wang
University of Adelaide, Australia and East China Normal University, Shanghai, China

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Abstract

We compare representations of the real and complex general linear groups and special linear groups in the framework of $K$ -theory, using base change on $L$ -parameters. We introduce a notion of base change on $K$ -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.

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

DOI 10.4171/JNCG/11-3-7