The Knapp-Stein Dimension Theorem for $p$-Adic Groups

The Knapp-Stein Dimension Theorem for $p$-Adic Groups

Knapp and Stein have proved for semisimple Lie groups that the dimension of the commuting algebra of an induced tempered representation equals the index of a certain reflection group in a larger group. A precise analogue of their result is stated and proved in this paper for $p$-adic groups.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Proceedings of the American Mathematical Society 1978-02, Vol.68 (2), p.243-246, Article 243
1. Verfasser: Silberger, Allan J.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Commuting
Mathematical functions
Mathematical theorems
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Knapp and Stein have proved for semisimple Lie groups that the dimension of the commuting algebra of an induced tempered representation equals the index of a certain reflection group in a larger group. A precise analogue of their result is stated and proved in this paper for $p$-adic groups.
ISSN:0002-9939
1088-6826
DOI:10.2307/2041781