Geometry

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By Dan Barbasch (auth.), Juan Tirao, David A. Vogan Jr., Joseph A. Wolf (eds.)

The illustration idea of Lie teams performs a crucial function in either clas­ sical and up to date advancements in lots of components of arithmetic and physics. In August, 1995, the 5th Workshop on illustration conception of Lie teams and its functions came about on the Universidad Nacional de Cordoba in Argentina. equipped via Joseph Wolf, Nolan Wallach, Roberto Miatello, Juan Tirao, and Jorge Vargas, the workshop provided expository classes on present examine, and person lectures on extra really good issues. the current vol­ ume displays the twin personality of the workshop. the various articles can be available to graduate scholars and others getting into the sector. here's a tough define of the mathematical content material. (The editors beg the indulgence of the readers for any lapses during this preface within the excessive criteria of ancient and mathematical accuracy that have been imposed at the authors of the articles. ) Connections among flag types and illustration thought for genuine re­ ductive teams were studied for nearly fifty years, from the paintings of Gelfand and Naimark on vital sequence representations to that of Beilinson and Bernstein on localization. the object of Wolf offers an in depth introduc­ tion to the analytic aspect of those advancements. He describes the development of normal tempered representations by way of square-integrable partly harmonic kinds (on yes actual staff orbits on a flag variety), and descriptions the components within the Plancherel formulation. ultimately, he describes fresh paintings at the advanced geometry of actual staff orbits on partial flag varieties.

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