Mathematical Sciences: Representation Theory of Reductive P-adic Groups

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This research concerns the classification of admissible representations of reductive p-adic groups in terms of their restrictions to compact-open subgroups. One of the goals of this work is to gain a good understanding of supercuspidal representations of these groups. The principal investigator continues his collaboration with Moy on the theory of minimal K-types, which is likely to play a fundamental role in representation theory of p-adic groups. The principal investigator also continues to pursue arithmetic, geometric and group-theoretic questions related to anisotropic semi-simple groups over global fields. 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 related objects which ape important in number theory and pure algebra.