Mathematical Sciences: Arithmetic Groups, P-adic Groups and Representation Theory

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This project is concerned with two related problems in the representation theory of p-adic groups. One is concerned with finding invariants of certain compact open subgroups in admissible representations of reductive groups over local fields. The other is concerned with the relationship between the Steinberg module of an algebraic Q-group, and the cohomology of its arithmetic subgroups. This research is in the area of representation theory of p-adic groups. The principal investigator will try to find invariants which measure certain properties of these groups. This work would have important implications for the theory of automorphic forms. It will be of interest to algebraists and number theorists alike.