
Journal of Lie Theory 29 (2019), No. 2, 473492 Copyright Heldermann Verlag 2019 The Algebraic MackeyHigson Bijections Eyal Subag Dept. of Mathematics, Penn State University, University Park, PA 16802, U.S.A. eus25@psu.edu For a linear connected semisimple Lie group G, we construct an explicit collection of correspondences between the admissible dual of G and the admissible dual of the Cartan motion group associated with G. We conjecture that each of these correspondences induces an algebraic isomorphism between the admissible duals. The constructed correspondences are defined in terms of algebraic families of HarishChandra modules. We prove that the conjecture holds in the case of SL_{2}(R), and, in that case, we characterize the bijections. Keywords: MackeyHigson bijection, algebraic families of HarishChandra pairs, algebraic families of HarishChandra modules. MSC: 22E47 [ Fulltextpdf (196 KB)] for subscribers only. 