Symmetries of CR sub-Laplacian

Abstract

We define a CR structure on a distinguished hyperplane in ${\mathbb{C}}^{n+1}$ and the CR sub-Laplacian on this CR manifold. We also define symmetries of the CR sub-Laplacian in general and for this special case construct all of them using the ambient construction. Then we investigate the algebra structure of the symmetry algebra of the sub-Laplacian. For this purpose we derive the decomposition of $S_0^k\mathfrak{sl}(V)$ under the action of $SL(V)$.

Cited by in corpus (2)

• Higher Symmetries of the Laplacian via Quantization
• Second Order Symmetries of the Conformal Laplacian