2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136627We use $G$-stable pieces to construct some equidimensional varieties and as a consequence, obtain Lusztig's dimension estimates \cite[section 4]{L2}. This is a generalization of \cite{HL}.8 pagesRepresentation Theory$G$-stable pieces and Lusztig's dimension estimatestext