Pizzetti formulae for Stiefel manifolds and applications
Abstract
Pizzetti's formula explicitly shows the equivalence of the rotation invariant integration over a sphere and the action of rotation invariant differential operators. We generalize this idea to the integrals over real, complex, and quaternion Stiefel manifolds in a unifying way. In particular we propose a new way to calculate group integrals and try to uncover some algebraic structures which manifest themselves for some well-known cases like the Harish-Chandra integral. We apply a particular case of our formula to an Itzykson-Zuber integral for the coset SO(4)/[SO(2)xSO(2)]. This integral naturally appears in the calculation of the two-point correlation function in the transition of the statistics of the Poisson ensemble and the Gaussian orthogonal ensemble in random matrix theory.
Keywords
Cite
@article{arxiv.1409.8207,
title = {Pizzetti formulae for Stiefel manifolds and applications},
author = {Kevin Coulembier and Mario Kieburg},
journal= {arXiv preprint arXiv:1409.8207},
year = {2015}
}