Spectral decomposition of L²(N∖GL(2),η)

Dinakar Ramakrishnan

Vol. 124 (1986), No. 1, 215–248

DOI: 10.2140/pjm.1986.124.215

Abstract

Let G denote GL(2,F), where F is R or C or a p-adic field. Let η be a non-trivial character of the unipotent upper triangular group N in G. The object of this paper is to present an explicit spectral decomposition of L²(N ∖G,η), the representation of G induced unitarily by η. This representation is well-known to be multiplicity-free and to be quasi-equivalent to the (right) regular representation of G.

Mathematical Subject Classification 2000

Primary: 22E45

Secondary: 11F72

Milestones

Received: 25 September 1981

Revised: 15 May 1984

Published: 1 September 1986