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

摘要

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. (C) 2015 Elsevier Ltd. All rights reserved.