Mathematical Sciences: Topics in Analysis on Real and P-Adic Lie Groups

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Professor Corwin will continue his investigations in harmonic analysis and representation theory for real nilpotent Lie groups and reductive p-adic groups. In the former area he will continue work with F. Greenleaf on homogeneous spaces of nilpotent Lie groups, particularly on problems characterizing the algebra of invariant differential operators for such spaces. Concerning p- adic groups, he will extend his work on supercuspidal representations. This problem is central in questions of representation theory for these groups. Professor Corwin's project involves questions in the representation theory of groups. Group theory is basically the study of symmetry. If a system looks the same from every point in space then the symmetry group contains the group of translations. In particular situations, a knowledge of the abstract group is not enough and one needs to consider concrete realizations of the group of transformations, in other words, a representation.