Geodesic
Trace Class Groups: the Case of Semi-Direct Products
Gerrit van Dijk1
1Mathematisch Instituut, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
Journal of Lie Theory, Tome 29 (2019) no. 2, pp. 375-390

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

A Lie group $G$ is called a trace class group if for every irreducible unitary representation $\pi$ of $G$ and every $C^\infty$ function $f$ with compact support the operator $\pi (f)$ is of trace class. In this paper we extend the study of trace class groups, begun in a previous paper, to special families of semi-direct products. For the case of a semisimple Lie group $G$ acting on its Lie algebra $\mathfrak g$ by means of the adjoint representation we obtain a nice criterion in order that $\mathfrak g \rtimes G$ is a trace class group.
Classification : 22D10, 22E30, 43A80
Mots-clés : Trace class group, Levi decomposition, semi-direct product, semisimple Lie group, orbit, invariant measure

Gerrit van Dijk  1

1 Mathematisch Instituut, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands 
Gerrit van Dijk. Trace Class Groups: the Case of Semi-Direct Products. Journal of Lie Theory, Tome 29 (2019) no. 2, pp. 375-390. http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a3/
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     author = {Gerrit van Dijk},
     title = {Trace {Class} {Groups:} the {Case} of {Semi-Direct} {Products}},
     journal = {Journal of Lie Theory},
     pages = {375--390},
     year = {2019},
     volume = {29},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2019_29_2_a3/}
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