Mathematical Sciences: Unipotent Representations of p-Adic Groups

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9622343 Reeder This award supports the research of Professor M. Reeder to work in automorphic functions. He intends to work on unipotent representations of reductive p-adic algebraic groups. He also intends to work on p-adic harmonic analysis. The idea here is to see how various computation relating to Plancheral measures relate to the geometry of the fixed point varieties of flag manifolds. Automorphic function theory arose out of Non-Euclidean geometry in the middle of the nineteenth century. Both mathematicians and physicists have thus long realized that many objects of fundamental importance are non-Euclidean in their basic nature. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots and thus to problems in areas as diverse as gauge theory in theoretical physics and coding theory in information theory. ??