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Journal of Lie Theory 29 (2019), No. 2, 473--492
Copyright Heldermann Verlag 2019

The Algebraic Mackey-Higson Bijections

Eyal Subag
Dept. of Mathematics, Penn State University, University Park, PA 16802, U.S.A.

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 Harish-Chandra modules. We prove that the conjecture holds in the case of SL2(R), and, in that case, we characterize the bijections.

Keywords: Mackey-Higson bijection, algebraic families of Harish-Chandra pairs, algebraic families of Harish-Chandra modules.

MSC: 22E47

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