Wonderful varieties of type B and C

TL;DR

This paper proves Luna's conjecture on classifying wonderful G-varieties of types B and C by reducing the problem to analyzing finitely many primitive cases and explicitly working out all such cases for classical groups.

Contribution

It provides a complete classification of wonderful varieties of types B and C by analyzing primitive cases for classical groups, confirming Luna's conjecture.

Findings

Reduction of Luna's conjecture to finitely many primitive cases

Explicit classification of primitive cases for classical groups

Confirmation of conjecture for types B and C

Abstract

We show that the proof of Luna's conjecture about the classification of general wonderful G-varieties can be reduced to the analysis of finitely many families of primitive cases. We work out all primitive cases arising with any classical group G.