
Journal of Lie Theory 23 (2013), No. 2, 493505 Copyright Heldermann Verlag 2013 A Plancherel Formula for Representative Functions on Semisimple Lie Groups Robert W. Donley, Jr. 344 Grove Street, #20, Jersey City, NJ 07306, U.S.A. rdonleyjr@gmail.com A Plancherel formula is given for representative functions on a connected semisimple Lie group G. Since the matrix coefficients for the irreducible finitedimensional representations are not necessarily squareintegrable, an alternative to the Schur Orthogonality Relations is given using invariant differential operators. The corresponding operator analysis is summarized. Keywords: Semisimple Lie group, Schur orthogonality relations, matrix coefficient, representative function, Plancherel formula. MSC: 22E46 [ Fulltextpdf (271 KB)] for subscribers only. 