Cubature formulas for great antipodal sets on complex Grassmann manifolds (Combinatorics of Lie Type)

Abstract

Great antipodal subsets of compact symmetric spaces are defined by Chen-Nagano [Trans. Amer. Soc. Math. (1988)] as finite subsets satisfying certain geometric properties with maximum cardinalities. In this paper, we give a formulation of Delsarte theory for finite subsets of compact symmetric spaces, and as its application, we show that great antipodal subsets of complex Grassmannian manifolds give cubature formulas for certain functional spaces.