Primitive spherical systems

Abstract

A spherical system is a combinatorial object, arising in the theory of wonderful varieties, defined in terms of a root system. All spherical systems can be obtained by means of some general combinatorial procedures (such as parabolic induction and wonderful fiber product) from the so-called primitive spherical systems. Here we classify the primitive spherical systems. As an application, we prove that the quotients of a spherical system are in correspondence with the so-called distinguished subsets of colors.