Mathematical Sciences: Representation Theory of Real Reductive Groups, L-groups and Reductive Dual Pairs

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9401074 Adams Adams will continue his work on the representation theory of real reductive Lie groups, with particular focus on the representation correspondence arising from real reductive dual pairs, generalizing recent work on complex groups and the dual pairs (O(p,q),Sp(2n,R) with p+q=2n+1. He will also investigate questions arising in connection with Arthur's conjectures. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact up on mathematics itself, particularly in analysis and number theory, and upon the oretical physics, especially quantum mechanics and elementary particle physics. ***