HCIZ integral formula as unitarity of a canonical map between reproducing kernel spaces

Abstract

In this article we prove that the Harish-Chandra-Itzykson-Zuber (HCIZ) integral formula is equivalent to the unitarity of a canonical map between invariant subspaces of Segal-Bargmann spaces. As a consequence, we provide two new proofs of the HCIZ integral formula and alternative proofs of related results.

arXiv comment12 pages, minor changes in the presentation of the previous version where made. References where added