Duality for the universal cover of Spin(2n + 1, 2n).

摘要

Let G=Spin4n+ 1,C be the connected, simply connected complex Lie group of type B2n and let G = Spin(2n + 1, 2n) denote its (connected) split real form. Then G has fundamental group Z2 and we denote the corresponding nonalgebraic double cover by G&d5;=Spin&d15; 2n+ 1,2n . The main purpose of this dissertation is to describe a latent symmetry in the set genuine representation theoretic parameters for G˜ at certain half-integral infinitesimal characters. This symmetry is then used to establish a duality of the corresponding generalized Hecke modules and ultimately results in a character multiplicity duality for the genuine characters of G˜.