Mathematical Sciences: The Schwartz Space of Real Reductive Lie Groups and the Theory of L-Groups

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The principal investigators plan to work on problems in mathematical analysis concerning 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, they will be working with real reductive Lie groups. Interactions with the theory of automorphic forms, for instance via the non-linear two-fold coverings of algebraic groups, will be explored. Work will continue on a project concerning the Schwartz space of reductive Lie groups, with emphasis on the infinite center case.