The heat kernel of the symmetric space \(\mathcal P_n\)
Let \({\mathcal P}_n\) be the set of all \(n\times n\) Hermite positive defined matrices. \({\mathcal P}_n\) is considered as a homogeneous space for the group \(GL(n)\) of nonsingular \(n\times n\) complex matrices and let \(\Delta\) be the Laplace-Beltrami operator associated with the invariant Riemann metric on \({\mathcal P}_n\). The author computes the heat kernel (that is, the fundamental solution to the heat equation \((\Delta-\partial_t)f=0\)) on \({\mathcal P}_n\).
scientific article; zbMATH DE number 1598740