ABSTRACT: We have found that a fairly substantial chunk of  the 19-century analysis - for example, results found in Watson's book on Bessel functions - are unified in a new model for a special series of unitary representations of G. The Hilbert space in question is always L_2 of the half-line R_+. The Laguerre polynomials defines the K-types, Bessel functions are Whittaker vectors and a Weyl group element defines the Hankel transform. What makes everything work is an application of a beautiful theorem of  Ed Nelson. In the case at hand, it enables one to go from a Lie algebra of differential
operators to unitary representations of G, thereby recovering the entire so-called holomorphic series for G.

For further information visit the Seminar web site at http://mystic.math.neu.edu/alexmart/rtrt.html  or contact Alex Martsinkovsky <alexmart@neu.edu>