Minimal bandwidth for $${\mathbb C}^*$$-actions on generalized Grassmannians

Abstract The bandwidth of a $${\mathbb C}^*$$ C ∗ -action polarized pair ( X , L ) is natural measure its complexity. In this paper, we study -actions on rational homogeneous spaces, determining which provide minimal bandwidth. We prove that the linked to smallest coefficient fundamental weight, in base simple roots, describes variety as marked Dynkin diagram. As direct application results Chow groups Cayley plane $$\mathrm{E}_6(6)$$ E 6 ( ) .