Some applications of CHEVIE to the theory of algebraic groups

TL;DR

This paper demonstrates how the CHEVIE computer algebra system aids in algebraic group theory, particularly in studying unipotent classes, Springer correspondence, and Lusztig families, by leveraging combinatorial structures in Lie theory.

Contribution

It showcases new applications of CHEVIE in algebraic groups, connecting computational tools with theoretical questions in Lie theory.

Findings

CHEVIE effectively computes unipotent classes.

It provides insights into Springer correspondence.

It helps analyze Lusztig families.

Abstract

The computer algebra system CHEVIE is designed to facilitate computations with various combinatorial structures arising in Lie theory, like finite Coxeter groups and Hecke algebras. We discuss some recent examples where CHEVIE has been helpful in the theory of algebraic groups, in questions related to unipotent classes, the Springer correspondence and Lusztig families.