B.Scott Crofts’s research while affiliated with University of California, Santa Cruz and other places

Let G = Spin[4n+1] be the connected, simply connected complex Lie group of type B2nand let G = Spin(p, q) (p + q = 4n + 1) denote a (connected) real form. If q ∉ (0, 1), G has a nontrivial fundamental group and we denote the corresponding nonalgebraic double cover by G = Spin(p, q). The main purpose of this paper is to describe a symmetry in the set of genuine parameters for the various G at certain half-integral infinitesimal characters. This symmetry is 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.