International Research Fellow Awards: Gauge Supergroups, Indecomposable Representations of Semidirect Product Lie Groups

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9703942 Conley The International Research Fellow Awards Program enables U.S. scientists and engineers to conduct three to twentyfour months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad. This award will support a twelve-month postdoctoral research visit by Dr. Charles H. Conley, of the University of Texas, Denton, to work with Dr. Moshe Flato at the Universite de Bourgogne in Dijon, France. Dr. Flato is a well-known expert in mathematical physics. Dr. Conley will study irreducible unitary representations of gauge supergroups. He is trying to generalize them to the setting of supergroups and supermanifolds. In addition, he will complete a study on indecomposable representations of semidirect project Lie groups. He will use the realizations he has found to show that the smooth indecomposable representations with a preunitary composition series may be completed to representations acting by bounded operators in a Hilbert space. In addition to his work with Dr. Flato, the PI will also be able to work with active groups in affine Kac-Moody Lie algebras, quantum groups, and star representations. ***