 
Summary: Transformation Groups, Vol. ?, No. ?, ??, pp. 1?? c Birkh¨auser Boston (??)
PARTITIONS OF THE WONDERFUL GROUP
COMPACTIFICATION
JIANGHUA LU
Department of Mathematics
The University of Hong Kong
Pokfulam Road, Hong Kong
jhlu@maths.hku.hk
MILEN YAKIMOV
Department of Mathematics
University of California
Santa Barbara, CA 93106, U.S.A.
yakimov@math.ucsb.edu
Abstract. We define and study a family of partitions of the wonderful compactification 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 of G and a: A1 A2 is an isomorphism. The partitions of G of Springer and Lusztig
correspond respectively to the triples (, , id) and (, , id).
Introduction
Let G be a connected semisimple algebraic group over an algebraically closed field
