Subelliptic Peter–Weyl and Plancherel theorems on compact, connected, semisimple Lie groups

Subelliptic Peter–Weyl and Plancherel theorems on compact, connected, semisimple Lie groups

We will study the connections between the elliptic and subelliptic versions of the Peter–Weyl and Plancherel theorems, in the case when the sub-Riemannian structure is generated naturally by the choice of a Cartan subalgebra. Along the way we will introduce and study the subelliptic Casimir operator...

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Veröffentlicht in:Nonlinear analysis 2015-10, Vol.126, p.131-142
1. Verfasser: Domokos, András
Format: Artikel
Sprache:eng
Schlagworte:
Joints
Lie groups
Nonlinearity
Operators
Semisimple Lie groups
Sub-Riemannian geometry
Subelliptic Laplacian
Theorems
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Beschreibung
Zusammenfassung:We will study the connections between the elliptic and subelliptic versions of the Peter–Weyl and Plancherel theorems, in the case when the sub-Riemannian structure is generated naturally by the choice of a Cartan subalgebra. Along the way we will introduce and study the subelliptic Casimir operator associated to the subelliptic Laplacian.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2015.04.010