Partitions of the wonderful group compactification

Abstract

We define and study a family of partitions of the wonderful compactification $\overline{G}$ of a semisimple algebraic group G of adjoint type. The partitions are obtained from subgroups of G × G associated to triples (A₁, A₂, a), where A₁ and A₂ are subgraphs of the Dynkin graph Γ of G and a : A₁ → A₂ is an isomorphism. The partitions of $\overline{G}$ of Springer and Lusztig correspond, respectively, to the triples (∅, ∅, id) and (Γ, Γ, id).