Abstract: When studying irreducible admissible representations of a semisimple Lie group, one interesting task is to construct small representations. One place to look for small representations is inside representations induced from one-dimensional representations of maximal parabolic subgroups. A natural way to produce a subrepresentation is as the kernel of a sufficiently symmetric operator. Specifically, we will look at the group SU(p,q) and a family of differential operators known as the Heisenberg wave operators. We will seek K-finite solutions to the differential operators, so the first step is to understand the K-finite functions that appear in the induced representation as a whole. The goal of the presentation will be to explain this first step.
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