Functoriality and \(K\)-theory for \(\text{GL}_n(\mathbb{R})\). (English) Zbl 1370.22016
From the text (with added references):
“In the general theory of automorphic forms, an important role is played by base change and automorphic induction, two examples of the principle of functoriality in the Langlands program [J. Bernstein (ed.) and S. Gelbart (ed.), An introduction to the Langlands program. Lectures presented at the Hebrew University of Jerusalem, Jerusalem, Israel, March 12–16, 2001. Boston, MA: Birkhäuser (2003; Zbl 1112.11028)]. Base change and automorphic induction have a global aspect and a local aspect [J. Arthur and L. Clozel, Simple algebras, base change, and the advanced theory of the trace formula. Princeton, NY: Princeton University Press (1989; Zbl 0682.10022)]. In this article, we focus on the archimedean case of base change and automorphic induction for the general linear group \(\mathrm{GL}_n(\mathbb R)\), and we investigate these aspects of functoriality at the level of \(K\)-theory. …This article is the archimedean companion of our previous article [J. Noncommut. Geom. 1, No. 3, 311–331 (2007; Zbl 1149.22015)]”.
“In the general theory of automorphic forms, an important role is played by base change and automorphic induction, two examples of the principle of functoriality in the Langlands program [J. Bernstein (ed.) and S. Gelbart (ed.), An introduction to the Langlands program. Lectures presented at the Hebrew University of Jerusalem, Jerusalem, Israel, March 12–16, 2001. Boston, MA: Birkhäuser (2003; Zbl 1112.11028)]. Base change and automorphic induction have a global aspect and a local aspect [J. Arthur and L. Clozel, Simple algebras, base change, and the advanced theory of the trace formula. Princeton, NY: Princeton University Press (1989; Zbl 0682.10022)]. In this article, we focus on the archimedean case of base change and automorphic induction for the general linear group \(\mathrm{GL}_n(\mathbb R)\), and we investigate these aspects of functoriality at the level of \(K\)-theory. …This article is the archimedean companion of our previous article [J. Noncommut. Geom. 1, No. 3, 311–331 (2007; Zbl 1149.22015)]”.
Reviewer: Anatoly N. Kochubei (Kyïv)
MSC:
| 22E50 | Representations of Lie and linear algebraic groups over local fields |
| 11F70 | Representation-theoretic methods; automorphic representations over local and global fields |
| 46L80 | \(K\)-theory and operator algebras (including cyclic theory) |
| 19K56 | Index theory |
| 22E45 | Representations of Lie and linear algebraic groups over real fields: analytic methods |
