On the analogy between real reductive groups and Cartan motion groups. II: Contraction of irreducible tempered representations
Afgoustidis, Alexandre (2020), On the analogy between real reductive groups and Cartan motion groups. II: Contraction of irreducible tempered representations, Duke Mathematical Journal, 169, 5, p. 897-960. 10.1215/00127094-2019-0071
TypeArticle accepté pour publication ou publié
Journal nameDuke Mathematical Journal
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)Attached to any reductive Lie group G is a "Cartan motion group" G0 − a Lie group with the same dimension as G, but a simpler group structure. A natural one-to-one correspondence between the irreducible tempered representations of G and the unitary irreducible representations of G0, whose existence had been suggested by Mackey in the 1970s, has recently been described by the author. In the present notes, we use the existence of a family of groups interpolating between G and G0 to realize the bijection as a deformation: for every irreducible tempered representation π of G, we build, in an appropriate Fr\'echet space, a family of subspaces and evolution operators that contract π onto the corresponding representation of G0.
Subjects / KeywordsCartan motion group; contractions of Lie groups; deformation of representations; Mackey analogy; Mackey–Higson bijection; real reductive groups; tempered representations
Showing items related by title and author.