Determinantal Expressions of Certain Integrals on Symmetric Spaces

Abstract

The integral of a function f defined on a symmetric space M≃ G/ K may be expressed in the form of a determinant (or Pfaffian),when f is K-invariant and, in a certain sense, a tensor power of a positive function of a single variable. The paper presents a few examples of this idea and discusses future extensions. Specifically, the examples involve symmetric cones, Grassmann manifolds, and classical domains.