2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78925The 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.68 pages; Dedicated to the memory of Irving E. SegalFunctional AnalysisMathematical Physicstext