Primitive spherical systems

Bravi, P.

doi:10.1090/S0002-9947-2012-05621-2

Primitive spherical systems
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Trans. Amer. Math. Soc. 365 (2013), 361-407 Request permission

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.

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