Mathematical Sciences: Representation Theory of Reductive p-adic Groups

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Professor Moy will investigate the unitarity question in the representation theory of certain kinds of groups. His work will focus on unipotent representations, reducibility problems related to unitarity, and the relationship of certain Hecke algebra isomorphisms to unitarity. Group theory is basically the study of symmetry. To take a simple example, when the system in question is invariant under a change in the position of the origin of space, the group of translations naturally arises. While groups are abstract objects, particular situations demand concrete realizations or "representations" of the symmetry group. Professor Moy's investigations involve certain special representations which enjoy a distance preserving property called unitarity.