%0 Journal Article %T Singular supports for character sheaves on a group compactification %A Xuhua He %A George Lusztig %J Mathematics %D 2005 %I arXiv %X Let $G$ be a semisimple adjoint group over $\bold C$ and $\bar{G}$ be the De Concini-Procesi completion of $G$. In this paper, we define a Lagrangian subvariety $\Lambda$ of the cotangent bundle of $\bar{G}$ such that the singular support of any character sheaf on $\bar{G}$ is contained in $\Lambda$. %U http://arxiv.org/abs/math/0511050v1