Mathematical Sciences: Representation Theory For Semisimple Lie Groups

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This project is mathematical research in the representation theory of Lie groups. A suitable example of the latter is the group of rotations of a sphere. Groups like this are important because they occur in many areas of mathematics ( e.g. geometry, differential equations,algebraic number theory, mathematical physics ) as groups of symmetries. Representation theory allows one to take advantage of symmetries in solving problems. More specifically, the three principal investigators will study algebraic and analytic localizations of representations, in the context of D-modules and Harish-Chandra modules. The overall theme is to get back and forth between various accounting schemes for the representations of a given group. This work involves techniques and ideas from several areas of mathematics, for instance algebraic geometry and complex geometry.