Journal of Noncommutative Geometry

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Volume 11, Issue 3, 2017, pp. 1001–1036
DOI: 10.4171/JNCG/11-3-7

Published online: 2017-09-26

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

Kuok Fai Chao[1] and Hang Wang

(1) Shanghai University, China

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.

Keywords: $K$-theory, local Langlands correspondence, base change, reduced group $C^*$-algebra, tempered representation

Chao Kuok Fai, Wang Hang: Langlands functorality in $K$-theory for $C^*$-algebras. I. Base change. J. Noncommut. Geom. 11 (2017), 1001-1036. doi: 10.4171/JNCG/11-3-7