On the generalised Springer correspondence for groups of type $E_8$

TL;DR

This paper completes the classification of the generalized Springer correspondence for groups of type E8 by proving Lusztig's conjecture on the remaining open cases, advancing understanding in algebraic group theory.

Contribution

It proves Lusztig's conjecture for the last unresolved cases of the generalized Springer correspondence in type E8 groups, filling a key gap in the theory.

Findings

Confirmed the last open cases of the Springer correspondence for E8.

Established new theoretical results supporting Lusztig's conjecture.

Enhanced the classification of algebraic group representations.

Abstract

We complete the determination of the generalised Springer correspondence for connected reductive algebraic groups, by proving a conjecture of Lusztig on the last open cases which occur for groups of type $E_8$.