Corpus ID: 54840100

On the analogy between real reductive groups and Cartan motion groups. I: The Mackey-Higson bijection

@article{Afgoustidis2015OnTA,
  title={On the analogy between real reductive groups and Cartan motion groups. I: The Mackey-Higson bijection},
  author={Alexandre Afgoustidis},
  journal={arXiv: Representation Theory},
  year={2015}
}
  • Alexandre Afgoustidis
  • Published 2015
  • Mathematics
  • arXiv: Representation Theory
  • George Mackey suggested in 1975 that there should be analogies between the irreducible unitary representations of a noncompact reductive Lie group $G$ and those of its Cartan motion group $G_0$ $-$ the semidirect product of a maximal compact subgroup of $G$ and a vector space. He conjectured the existence of a natural one-to-one correspondence between "most" irreducible (tempered) representations of $G$ and "most" irreducible (unitary) representations of $G_0$. We here describe a simple and… CONTINUE READING
    7 Citations

    Figures from this paper

    References

    SHOWING 1-10 OF 51 REFERENCES
    On the Analogy Between Complex Semisimple Groups and Their Cartan Motion Groups
    • 15
    • PDF
    Classification of the irreducible representations of semisimple Lie groups.
    • D. Vogan
    • Mathematics, Medicine
    • Proceedings of the National Academy of Sciences of the United States of America
    • 1977
    • 11
    • PDF
    Analysis on homogeneous spaces and representation theory of Lie Groups, Okayama-Kyoto
    • 26
    • Highly Influential
    A proof of Blattner's conjecture
    • 132
    Contractions of representations of de Sitter groups
    • 76
    Spherical functions on Cartan motion groups
    • 7
    • PDF
    On contractions of semisimple Lie groups
    • 63
    • PDF
    The Campbell-Hausdorff formula and invariant hyperfunctions
    • 89
    • PDF
    THE MACKEY ANALOGY AND K-THEORY
    • 21
    • PDF