This publication brings jointly 5 papers which were influential within the examine of Lie teams. although released greater than twenty years in the past, those papers made primary contributions that deserve a lot broader publicity. furthermore, the next literature that has subsumed those papers can't exchange the originality and energy they include. The editors have supplied a quick creation to every paper, in addition to a synopsis of the key advancements that have happened within the region coated by way of every one paper. incorporated listed here are the doctoral theses of Arthur, Osborne, and Schmid. Arthur's thesis is heavily with regards to Trombi's paper insofar as either take care of harmonic research on actual semisimple Lie teams, and, particularly, research at the Schwartz area of Harish-Chandra. Arthur's thesis is anxious with the picture lower than the Fourier remodel of the Schwartz area of a semisimple Lie workforce of actual rank one, whereas Trombi's paper offers an expository account of the harmonic research linked to the decomposition of the Schwartz house below the normal illustration. In his thesis, Osborne extends the Atiyah-Bott mounted aspect theorem for elliptic complexes to acquire a set element formulation for complexes that aren't elliptic. Schmid proves a generalization of the Borel-Weil theorem referring to an particular and geometric attention of the irreducible representations of a compact, hooked up semisimple Lie workforce. Langlands's primary paper offers a category of irreducible, admissible representations of actual reductive Lie teams.
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