Resumen de Volumes of principal orbits of isotropy subgroups in compact symmetric spaces

Balázs Csikós, Brigitta Németh, László Verhóczki

• Let (G,K) be a Riemannian symmetric pair of compact type such that G is simply connected. Take the compact Riemannian symmetric space G/K and the natural isometric action of the isotropy subgroup K on G/K. In this paper, we discuss the problem how to compute the volumes of the principal orbits in explicit form and how to find the unique principal orbit of maximal volume. Moreover, we study this problem in detail in some rank two irreducible symmetric spaces with different restricted root systems.