The algebraic Mackey-Higson bijections

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)473-492
Number of pages20
JournalJournal of Lie Theory
Volume29
Issue number2
StatePublished - Jan 1 2019

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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