Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 014, 9 pages      arXiv:2003.13512      https://doi.org/10.3842/SIGMA.2021.014

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

Fabrice Baudoin and Gunhee Cho
Department of Mathematics, University of Connecticut, 196 Auditorium Road, Storrs, CT 06269-3009, USA

Received July 31, 2020, in final form January 29, 2021; Published online February 10, 2021

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.

Key words: sub-Laplacian; 15-dimensional octonionic anti-de Sitter space; the anti-de Sitter fibration.

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