Analysis in matrix space and Speh's representations
The unitary representations of GL(n,R) are obtained, via unitary parabolic induction, from a tensor product of unitary representations which are either one-dimensional, special (``Speh'') or a complementary series representation constructed from one of these. In this paper an explicit realization of the special representations is constructed using harmonic analysis. As a consequence it is shown that every unitary representation of GL(n,R) remains irreducible upon restriction to the subgroup \(P_ n\) consisting of matrices whose last row is (0,...,0,1). This had been conjectured by A. Kirillov in 1962.
scientific article; zbMATH DE number 4202613
scientific article