Mathematical Sciences: The Combinatoric Structure of Representations of Semi-Simple Groups Over Valued Fields

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This research is in the area of group representation theory. The principal investigator will develop an algebraic harmonic analysis to transfer the representation theory of semisimple groups to the representation theory of Hecke algebras. The central problem to be considered in this project is the Lusztig conjecture which states that certain invariants attached to an algebraic group can be calculated from polynomials. This is a difficult and central problem in group theory. It also has implications in other areas of mathematics.