$G$-stable pieces and Lusztig's dimension estimates

TL;DR

This paper utilizes G-stable pieces to construct equidimensional varieties, leading to a generalization of Lusztig's dimension estimates, thereby advancing understanding in algebraic geometry and representation theory.

Contribution

It introduces a new approach using G-stable pieces to generalize Lusztig's dimension estimates for algebraic varieties.

Findings

Construction of equidimensional varieties using G-stable pieces

Generalization of Lusztig's dimension estimates

Enhanced understanding of algebraic group actions

Abstract

We 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}.