Geodesic
On the Unitary Representation Theory of Locally Compact Contraction Groups
Max Carter1
1Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, Louvain-la-Neuve, Belgique
Journal of Lie Theory, Tome 34 (2024) no. 4, pp. 911-956

Voir la notice de l'article provenant de la source Heldermann Verlag

The unitary representation theory of locally compact contraction groups and their semi-direct products with Z is studied. We put forward the problem of completely characterising such groups which are type I or CCR and this article provides a stepping stone towards a solution to this problem. In particular, we determine new examples of type I and non-type-I groups in this class, and we completely classify the irreducible unitary representations of the torsion-free groups, which are shown to be type I. When these groups are totally disconnected, they admit a faithful action by automorphisms on an infinite locally-finite regular tree; this work thus provides new examples of automorphism groups of regular trees with interesting representation theory, adding to recent work on this topic.
Classification : 20C25, 22D10, 22D12, 22D25, 20G05, 43A65
Mots-clés : Unitary representation, type I group, CCR group, scale group, contraction group, unipotent linear algebraic group, amenable group, groups acting on trees

Max Carter  1

1 Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, Louvain-la-Neuve, Belgique 
Max Carter. On the Unitary Representation Theory of Locally Compact Contraction Groups. Journal of Lie Theory, Tome 34 (2024) no. 4, pp. 911-956. http://geodesic.mathdoc.fr/item/JOLT_2024_34_4_a7/
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     title = {On the {Unitary} {Representation} {Theory} of {Locally} {Compact} {Contraction} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {911--956},
     year = {2024},
     volume = {34},
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     url = {http://geodesic.mathdoc.fr/item/JOLT_2024_34_4_a7/}
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