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

Abstract

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.

This note completes the study of the sub-Laplacians and associated heat kernels for the sub-Riemannian structures coming from H-type submersions over rank-one symmetric spaces. This is the companion of arXiv:1904.08568 which concerned the octonionic Hopf fibration and follows arXiv:1805.06796 and arXiv:1204.3642