Polynomial representations and associated cycles for indefinite unitary groups

The associated variety is a geometric invariant attached to each Harish-Chandra module of a real reductive Lie group. The associated cycle is a ner invariant that gives additional algebraic data for each component of the associated variety. The main result of this thesis is a set of formulas for associated cycles of a large class of Harish-Chandra modules for the real Lie group U(p; q). These formulas give the associated cycle polynomials for the coherent family containing a module X when elements of the dense orbit in the associated variety of X have a single nontrivial Jordan block or exactly two Jordan blocks.