Subelliptic Peter-Weyl and Plancherel theorems on compact, connected, semisimple Lie groups. (English) Zbl 1377.22008
Summary: 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.
MSC:
| 22E30 | Analysis on real and complex Lie groups |
| 35R03 | PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. |
References:
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