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

TL;DR

This paper derives explicit formulas for the heat kernel on quaternionic projective spaces by establishing integral representations for Jacobi polynomials, advancing the understanding of heat diffusion in these geometric settings.

Contribution

It provides the first explicit integral and expansion formulas for the heat kernel on quaternionic projective spaces, utilizing new representations of Jacobi polynomials.

Findings

Explicit integral representation of the heat kernel $H_n(t;x,y)$

Expansion formulas for the heat kernel

New integral representation for Jacobi polynomials of type $P_l^{(2n-1,1)}$

Abstract

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 $\mathbb{P}^n(\mathbb H)$, $n \geq 1$. This was possible by establishing a real integral representation formula for Jacobi polynomials of type $P_l^{(2n-1,1)}(\cos(2d))$.