This paper is devoted to the role played by the Higgs algebra H3 in the generalisation of classical harmonic analysis from the sphere Sm-1 to the (oriented) Grassmann manifold Gr o(m, 2) of 2-planes. This algebra is identified as the dual partner (in the sense of Howe duality) of the orthogonal group SO (m) acting on functions on the Grassmannian. This is then used to obtain a Pizzetti formula for integration over this manifold. The resulting formulas are finally compared to formulas obtained earlier for the Pizzetti integration over Stiefel manifolds, using an argument involving symmetry reduction.
ASJC Scopus subject areas
- Political Science and International Relations
- Geometry and Topology