Designs in Grassmannian spaces and lattices (Q1862267)

The authors generalise the notion of spherical design due to \textit{P. Delsarte}, \textit{J. M. Goethals} and \textit{J. J. Seidel} [Geom. Dedicata 6, 363--388 (1977; Zbl 0376.05015)]. They define and characterise \(t\)-designs on a Grassmann manifold of \({\mathbb R}^n\) . Furthermore they characterise the finite subgroups of the orthogonal group such that each orbit is such a \(t\)-design and investigate some relationship between certain \(4\)-designs and the Rankin functions. The paper is endowed with interesting examples.