Langlands functorality in K-theory for C∗-algebras. I. Base change

Kuok Fai Chao; Hang Wang

doi:10.4171/JNCG/11-3-7

Langlands functorality in K-theory for C∗-algebras. I. Base change

Kuok Fai Chao
, Hang Wang

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1001-1036
Number of pages	36
Journal	Journal of Noncommutative Geometry
Volume	11
Issue number	3
DOIs	https://doi.org/10.4171/JNCG/11-3-7
State	Published - 2017

Keywords

Base change
K-theory
Local Langlands correspondence
Reduced group C∗-algebra
Tempered representation

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10.4171/JNCG/11-3-7

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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.",

keywords = "Base change, K-theory, Local Langlands correspondence, Reduced group C∗-algebra, Tempered representation",

author = "Chao, \{Kuok Fai\} and Hang Wang",

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AU - Wang, Hang

N1 - Publisher Copyright: © European Mathematical Society.

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

KW - Base change

KW - K-theory

KW - Local Langlands correspondence

KW - Reduced group C∗-algebra

KW - Tempered representation

UR - https://www.scopus.com/pages/publications/85030115724

U2 - 10.4171/JNCG/11-3-7

DO - 10.4171/JNCG/11-3-7

M3 - 文章

AN - SCOPUS:85030115724

SN - 1661-6952

VL - 11

SP - 1001

EP - 1036

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

IS - 3

ER -

Langlands functorality in K-theory for C∗-algebras. I. Base change

Abstract

Keywords

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