1999/08/06 by Palle E. T. Jorgensen, Gestur Ólafsson
Mathematics · Physics and Astronomy · #math.FA #math-ph #math.MP
published as The Mathematical Legacy of Harish-Chandra: A Celebration of Representation Theory and Harmonic Analysis (R. Doran and V. Varadarajan, eds.), Proc. Sympos. Pure Math., vol. 68, American Mathematical Society, Providence, R.I., 2000, pp. 333--401. · 68 pages; Dedicated to the memory of Irving E. Segal
arxiv created 1999/08/06 · arxiv updated 2009/11/30
The notions of reflection, symmetry, and positivity from quantum field theory are shown to induce a duality operation for a general class of unitary representations of Lie groups. The semisimple Lie groups which have this c-duality are identified and they are placed in the context of Harish-Chandra's legacy for the unitary representations program. Our paper begins with a discussion of path space measures, which is the setting where reflection positivity (Osterwalder-Schrader) was first identified as a useful tool of analysis.