On the analogy between real reductive groups and Cartan motion groups. I: The Mackey-Higson bijection
Afgoustidis, Alexandre (2021), On the analogy between real reductive groups and Cartan motion groups. I: The Mackey-Higson bijection. https://basepub.dauphine.psl.eu/handle/123456789/22322
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-01214358
Series titleCahier de recherche du CEREMADE
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)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 G0 − 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 G0. We here describe a simple and natural bijection between the tempered duals of both groups, and an extension to a one-to-one correspondence between the admissible duals.
Subjects / KeywordsRepresentations of semisimple Lie groups; Lie group contractions; Mackey analogy; Tempered dual
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On the analogy between real reductive groups and Cartan motion groups. II: Contraction of irreducible tempered representations Afgoustidis, Alexandre (2020) Article accepté pour publication ou publié