Lusztig's conjecture for finite special linear groups

2005/02/09 by Toshiaki Shoji, Shoji, Toshiaki
Mathematics · #20G05 #20G40 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Representation Theory (math.RT) #math.RT #msc:20G05 #msc:20G40

paper · pdf · doi:10.48550/arxiv.math/0502180

65 pages

arxiv created 2005/02/09 · openalex publication_date 2005/02/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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