K-types of SU(1,n) representations and restriction of cohomology

Mark R. Sepanski

Vol. 192 (2000), No. 2, 385–398

DOI: 10.2140/pjm.2000.192.385

Abstract

This paper shows that the highest weights of the K-types of any irreducible admissible representation of SU(1,n) are determined by certain restriction maps from u to u ∩ k cohomology. In particular, the image of these maps determines a set of points in a Cartan subalgebra. It is proved that the highest weights of the K-types are given by intersecting a translate of the root lattice with the closed convex hull of the points determined by the restriction maps.

Milestones

Received: 4 June 1998

Revised: 19 August 1998

Published: 1 February 2000