The Subelliptic Heat Kernel of the Octonionic Anti-De Sitter Fibration

In this note, we study the sub-Laplacian of the 15-dimensional octonionic anti-de Sitter space which is obtained by lifting with respect to the anti-de Sitter fibration the Laplacian of the octonionic hyperbolic space $\mathbb{O}{H}^1$. We also obtain two integral representations for the corresponding subelliptic heat kernel.