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 $S^{k}_{0}\mathfrak{sl}(V)$ under the action of $SL(V)$.