### 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 SL_{2}(R), and, in that case, we characterize the bijections.

Original language | English (US) |
---|---|

Pages (from-to) | 473-492 |

Number of pages | 20 |

Journal | Journal of Lie Theory |

Volume | 29 |

Issue number | 2 |

State | Published - Jan 1 2019 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

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*Journal of Lie Theory*, vol. 29, no. 2, pp. 473-492.

**The algebraic Mackey-Higson bijections.** / Subag, Eyal Moshe.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The algebraic Mackey-Higson bijections

AU - Subag, Eyal Moshe

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85068940605&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85068940605&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85068940605

VL - 29

SP - 473

EP - 492

JO - Journal of Lie Theory

JF - Journal of Lie Theory

SN - 0949-5932

IS - 2

ER -