Geodesic
Designs in Grassmannian spaces and lattices
Journal of Algebraic Combinatorics, Tome 16 (2002) no. 1, pp. 5-19.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We introduce the notion of a $t$-design on the Grassmann manifold $G _{ m, n}$ mathcalG_m,n of the $m$-subspaces of the Euclidean space $\mathbb R$ mathbbR $^{ n }$. It generalizes the notion of antipodal spherical design which was introduced by P. Delsarte, J.-M. Goethals and J.-J. Seidel. We characterize the finite subgroups of the orthogonal group which have the property that all its orbits are $t$-designs. Generalizing a result due to B. Venkov, we prove that, if the minimal $m$-sections of a lattice $L$ form a 4-design, then $L$ is a local maximum for the Rankin function $gamma_{ n,m }$.
Keywords: lattice, Grassmann manifold, orthogonal group, zonal function 
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     title = {Designs in {Grassmannian} spaces and lattices},
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Bachoc, Christine; Coulangeon, Renaud; Nebe, Gabriele. Designs in Grassmannian spaces and lattices. Journal of Algebraic Combinatorics, Tome 16 (2002) no. 1, pp. 5-19. http://geodesic.mathdoc.fr/item/JAC_2002__16_1_a6/