TY  - Type of reference 
TI  - Explicit formulas of the heat kernel on the quaternionic projective spaces 
AU  - Ali Hafoud  
AU  -  Allal Ghanmi 
AB  - We consider the heat equation on the quaternionic projective space $$$P_{n}(ℍ)$$$, and we establish two formulas for the heat kernel, a series expansion involving Jacobi polynomials, and an integral representation involving a $$$\theta$$$-function. More precisely, using the quaternonic Hopf fibration and the explicit integral representation of the heat kernel on the complex projective space $$$P_{2n+1}(ℂ)$$$, as well as an integral representation of Jacobi polynomials in terms of Gegenbauer polynomials, we give an explicit integral representation of the heat kernel on the $$$n$$$-quaternionic projective space. We also establish an explicit series expansion of the heat kernel in terms of the Jacobi polynomials. Moreover, we derive an explicit formula of the heat kernel on the sphere $$$S^4$$$. 
DO  - 10.21494/ISTE.OP.2022.0809 
JF  - Advances in Pure and Applied Mathematics 
KW  - Heat equation,  Heat kernel,  Quaternionic projective space,  Hopf fibration,  Jacobi polynomials, Heat equation,  Heat kernel,  Quaternionic projective space,  Hopf fibration,  Jacobi polynomials,  
L1  - http://www.openscience.fr/IMG/pdf/iste_apam22v13n2_1.pdf 
LA  - en 
PB  - ISTE OpenScience 
DA  - 2022/03/14 
SN  - 1869-6090 
TT  - Formules explicites du noyau de la chaleur sur les espaces projectifs des quaternions 
UR  - http://www.openscience.fr/Explicit-formulas-of-the-heat-kernel-on-the-quaternionic-projective-spaces 
IS  - Issue 2 (March 2022) 
VL  - 13 
ER  -