Application of restriction of Fourier transforms to an example from representation theory

L. Barchini and Mark R. Sepanski

Vol. 198 (2001), No. 2, 265–294

DOI: 10.2140/pjm.2001.198.265

Abstract

This paper uses restriction of Fourier transforms to construct explicit realizations of certain irreducible unitary representations of SU(n,n). The realizations begin with generalizations of the classical Szegö map. Boundary values of these Szegö maps naturally lead to certain restrictions of Fourier transforms.  The image of these restrictions provide concrete constructions of unitary representations as L² spaces on certain orbits. The SU(n,n) invariance of the L² spaces and inner products follows immediately from the restriction maps and the natural pairing between certain degenerate principal series.

Milestones

Received: 20 August 1999

Revised: 24 February 2000

Published: 1 April 2001