Mathematical Sciences: Representation Theory of P-adic Groups

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This project is concerned with the admissible representation theory of reductive groups over p-adic fields and, in particular, the various correspondences between the sets of irreducible representations of these groups. The principal investigators will work on the classification of the admissible dual via restriction to certain compact, open subgroups; relations with parabolic induction; and compatibility with Langlands functoriality and Howe's theory of the theta correspondence. This research falls into the broad category of p-adic algebraic groups. Historically, algebraic groups arose in an effort to describe all the transformations or symmetries of an n-dimensional space. The spaces under consideration here, however, are not the familiar real spaces like the line and the plane, but totally disconnected objects that are important in number theory and pure algebra.