Lusztig's conjecture for finite special linear groups

TL;DR

This paper proves Lusztig's conjecture for finite special linear groups, showing the equivalence of characteristic functions of character sheaves and almost characters, and provides explicit scalar computations for character determination.

Contribution

It establishes Lusztig's conjecture for finite special linear groups and offers a method to compute their irreducible characters.

Findings

Characteristic functions of character sheaves match almost characters.

Explicit scalars are determined for the matching.

Provides a practical method for computing irreducible characters.

Abstract

In this paper, we prove Lusztig's conjecture for finite special linear groups, i.e., we show that characteristic functions of character sheaves coincide with almost characters up to scalar constants, under the condition that the characteristic of the base field is not too small. We determine those scalars explicitly. Our result gives a method of computing irreducible characters of these groups.