Functoriality and K-theory for GL_n(R)

DOI10.17879/33249453612zbMATH Open1370.22016arXiv1510.03662OpenAlexW2209569501MaRDI QIDQ5738304

Sérgio Mendes, Roger Plymen

Publication date: 9 June 2017

Abstract: We investigate base change and automorphic induction $mathbbC/mathbbR$ at the level of K-theory for the general linear group $G{L}_n(mathbbR)$. In the course of this study, we compute in detail the C*-algebra K-theory of this disconnected group. We investigate the interaction of base change with the Baum-Connes correspondence for $G{L}_n(mathbbR)$ and $G{L}_n(mathbbC)$. This article is the archimedean companion of our previous article in the Journal of Noncommutative Geometry.

Full work available at URL: https://arxiv.org/abs/1510.03662

zbMATH Keywords

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Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Representations of Lie and linear algebraic groups over local fields (22E50) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Index theory (19K56)

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