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.

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