Mathematical Sciences: Analysis on Semisimple Groups

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Professor Knapp will make systematic use of intertwining operators into and out of reducible and irreducible representations of semisimple Lie groups in order to understand the representations better. Two specific areas of investigation are the relationship of algebraic and analytic forms of representations and the introduction of a more direct approach to harmonic analysis on semisimple symmetric spaces. The postdoctoral associate supported by this award will use micro-local analysis to gain a better understanding of the dual of a semisimple Lie group. The research supported by this award is in the area of the representation theory of groups. Groups usually arise as transformations which preserve the structure of some system. For example, the group of rotations about the center preserves the sphere. In applications the abstract group is not all that is needed but in addition a concrete realization of this group, called a representation. This project will study the representations which arise from a family of smooth groups called Lie groups.