Formules explicites du noyau de la chaleur sur l'espace projectif quaternionique

In this note we give an explicit integral representation and an expanssion for the heat kernel $H_n(t;x,y)$ associated to Fubini-Study Laplacians on quaternionic projective spaces ${\mathbb{P}}^n(\mathbb{H})$, $n\ge 1$. This was possible by establishing a real integral representation formula for Jacobi polynomials of type $P_l^{(2n-1,1)}(\cos (2d))$.