Radial Laplacian on rotation groups - Archive ouverte HAL Accéder directement au contenu
Chapitre D'ouvrage Année : 2023

Radial Laplacian on rotation groups

Pierre Degond

Résumé

The Laplacian on the rotation group is invariant by conjugation. Hence, it maps class functions to class functions. A maximal torus consists of block diagonal matrices whose blocks are planar rotations. Class functions are determined by their values of this maximal torus. Hence, the Laplacian induces a second order operator on the maximal torus called the radial Laplacian. In this paper, we derive the expression of the radial Laplacian. Then, we use it to find the eigenvalues of the Laplacian, using that characters are class functions whose expressions are given by the Weyl character formula. Although this material is familiar to Lie-group experts, we gather it here in a synthetic and accessible way which may be useful to non experts who need to work with these concepts.
Fichier principal
Vignette du fichier
RadLap_arxiv.pdf (392.66 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03968776 , version 1 (01-02-2023)

Identifiants

  • HAL Id : hal-03968776 , version 1

Citer

Pierre Degond. Radial Laplacian on rotation groups. Particle Systems and Partial Differential Equations X (E. Carlen, P. Goncalves and A-J. Soares editors), Springer, In press, Springer Proceedings in Mathematics and Statistics. ⟨hal-03968776⟩
9 Consultations
12 Téléchargements

Partager

Gmail Facebook X LinkedIn More