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

SIGMA 17 (2021), 014, 9 pages      arXiv:2003.13512

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

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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  1. Baudoin F., Cho G., The subelliptic heat kernel of the octonionic Hopf fibration, Potential Anal., to appear, arXiv:1904.08568.
  2. Baudoin F., Demni N., Integral representation of the sub-elliptic heat kernel on the complex anti-de Sitter fibration, Arch. Math. (Basel) 111 (2018), 399-406, arXiv:1802.04199.
  3. Baudoin F., Demni N., Wang J., The horizontal heat kernel on the quaternionic anti-de Sitter spaces and related twistor spaces, Potential Anal. 52 (2020), 281-300, arXiv:1805.06796.
  4. Baudoin F., Grong E., Molino G., Rizzi L., $H$-type foliations, arXiv:1812.02563.
  5. Baudoin F., Wang J., Stochastic areas, winding numbers and Hopf fibrations, Probab. Theory Related Fields 169 (2017), 977-1005, arXiv:1602.06470.
  6. Bădiţoiu G., Ianuş S., Semi-Riemannian submersions from real and complex pseudo-hyperbolic spaces, Differential Geom. Appl. 16 (2002), 79-94, arXiv:math.DG/0005228.
  7. Eldredge N., Precise estimates for the subelliptic heat kernel on $H$-type groups, J. Math. Pures Appl. 92 (2009), 52-85, arXiv:0810.3218.
  8. Intissar A., Ould Moustapha M.V., Explicit formulae for the wave kernels for the Laplacians $\Delta_{\alpha\beta}$ in the Bergman ball $B^n$, $n\geq 1$, Ann. Global Anal. Geom. 15 (1997), 221-234.
  9. Tian Y., Matrix representations of octonions and their applications, Adv. Appl. Clifford Algebras 10 (2000), 61-90, arXiv:math.RA/0003166.
  10. Wang J., The subelliptic heat kernel on the anti-de Sitter space, Potential Anal. 45 (2016), 635-653, arXiv:1204.3642.

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